Revisions to How to solve a system of partial differential equations?

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edited Feb 15, 2017 at 2:22

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Edit: since the upgrade to Mathematica 10, this problem seems solved

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:=    DSolve[
    {
        D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
        (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
        (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
    }, f[a, b, c], {a, b, c}]

Out[1]=    
(* DSolve[
    {
        Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
        Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
        (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
    }, f[a, b, c], {a, b, c}] *)

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

Edit: since the upgrade to Mathematica 10, this problem seems solved

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

Edit: since the upgrade to Mathematica 10, this problem seems solved

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

    DSolve[
    {
        D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
        (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
        (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
    }, f[a, b, c], {a, b, c}]

    
(* DSolve[
    {
        Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
        Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
        (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
    }, f[a, b, c], {a, b, c}] *)

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

adding a note, problem solved since the upgrade to Mathematica 10

Source Link

edited Aug 10, 2014 at 23:54

mlpo

879
2
7
11

Edit: since the upgrade to Mathematica 10, this problem seems solved

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

Edit: since the upgrade to Mathematica 10, this problem seems solved

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

Tweeted twitter.com/#!/StackMma/status/434501296520175616

occurred Feb 15, 2014 at 1:35

add solution

Source Link

edited Feb 14, 2014 at 21:57

mlpo

879
2
7
11

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

I just want to solve a system of partial differential equations, for example:

$$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ \frac{1}{a} \times \frac{\partial}{\partial b}[f(a, b, c)] = 4 \cos(c) \sin(2b) \\ \frac{1}{a \sin(b)} \times \frac{\partial}{\partial c}[f(a, b, c)] = -4 \sin(b) \sin(c) \\ \end{array} \right. $$

And when I try to solve this system in Mathematica, the output does not help:

In[1]:= DSolve[
{
    D[f[a, b, c], a] == 4 Sin[b]^2 Cos[c],
    (1/a) *D[f[a, b, c], b] == 4 Cos[c] Sin[2 b],
    (1/(a Sin[b]))*D[f[a, b, c], c] == -4 Sin[b] Sin[c]
}, f[a, b, c], {a, b, c}]

Out[1]= DSolve[
{
    Derivative[1, 0, 0][f][a, b, c] == 4*Cos[c]*Sin[b]^2,
    Derivative[0, 1, 0][f][a, b, c]/a == 4*Cos[c]*Sin[2*b],
    (Csc[b]*Derivative[0, 0, 1][f][a, b, c])/a == -4*Sin[b]*Sin[c]
}, f[a, b, c], {a, b, c}]

Obviously, this output is useless… Probably I doing something wrong…

Thank you for your help

Note : The solution is $f(a, b, c) = 4a \sin^2(b) \cos(c) + K$ (K : the integration constant).

Source Link

asked Feb 14, 2014 at 21:43

mlpo

879
2
7
11

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