All Questions
4
questions
0
votes
2
answers
80
views
How can I handle$~\exp(\ln|x|)~$to solve 1st order linear DE?
RHS and LHS are same.
$$\exp\left(\ln\left(x\right)\right)=\exp\left(\ln\left(x\right)\right)\tag{1}$$
Taking log.
$$\ln\left(\exp\left(\ln\left(x\right)\right)\right)=\ln\left(\exp\left(\ln\left(x\...
- 1,519
1
vote
2
answers
48
views
Find the range of $y$ in a DE
Consider the equation $$y' = y^2 - y - 2 = (y+1)(y-2).$$ If $y(10) = 0$, find the range of $y(t)$ for $t>10$. That is, find the best $A$ and $B$ such that $A<y(t)<B$ for $t>10$.
From ...
- 329
1
vote
1
answer
115
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Can modulus function present in a particular solution
Particular solution of $2ye^{\tfrac{x}{y}}dx+\Big(y-2xe^{\tfrac{x}{y}}\Big)dy=0$, $x=0$ when $y=1$
Attempt
Put $x=vy$
$$
\frac{dx}{dy}=\frac{x}{y}-\frac{1}{2e^{\tfrac{x}{y}}}\\
\frac{dx}{dy}=v+y\...
- 7,674
2
votes
2
answers
129
views
Solution of $\frac{\mathrm{d}y}{\mathrm{d}x}=y\mathrm{e}^x$ given $x=0$, $y=\mathrm{e}$
$\dfrac{\mathrm{d}y}{\mathrm{d}x}=y\mathrm{e}^x$, $x=0$ and $y=\mathrm{e}$. Find the particular solution.
Attempt 1
$$
\dfrac{\mathrm{d}y}{\mathrm{d}x}=y\mathrm{e}^x\implies\dfrac{\mathrm{d}y}{y}=\...
- 7,674