All Questions
5
questions
1
vote
0
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45
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Tan of sum using differential equations
Define $S(x)$ and $C(x)$ as exponential functions, and $T(x) = S(x)/C(x)$. We want to derive the formula for $T(x+y)$, but the exercise I'm working on suggests setting up a differential equation $g(T(...
- 133
0
votes
1
answer
59
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For which input signals is the response resonant?
Consider the differential equation $y''' + 5y'' + 8y' + 6y = f(x)$.
For which following input signals $f(x)$ is the response resonant? Choose all those that apply.
$e^x, e^{-x}, e^{3x}, e^{-3x}, e^x\...
- 4,581
1
vote
2
answers
111
views
Solving $y'' + 2y' + 2y = 0$: How to eliminate imaginary unit from solution?
$$y'' + 2y' + 2y = 0$$
$\downarrow$ (write characteristic equation)
$\lambda^2 +2\lambda + 2 = 0$
$\downarrow$ (solve characteristic equation)
$\lambda = -1 \pm i$
$\downarrow$ (write general ...
- 1,922
1
vote
6
answers
198
views
General solution for $\frac{\mathrm{d}^2 y}{\mathrm{d} x^2} = y$?
Start with
$$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2} = y$$
then
$$\frac{1}{\mathrm{d} x} \, \mathrm{d} \left(\frac{\mathrm{d} y }{\mathrm{d} x}\right) = y$$
$$\frac{\mathrm{d} y}{\mathrm{d} x} \, \...
- 1,324
1
vote
1
answer
127
views
Which function to kill: Sine or Cos?
I got an equation which was a solution to some familiar Differential Equation I am solving, the solution takes the form of:
$$V=Ce^{-ix}$$
but
$$Ce^{-ix}=A\cos(x)+B\sin(x)$$
so
$$V=A\cos(x)+B\sin(...
- 211