- #1

Rumpelstiltzkin

- 17

- 0

Here's the problem:

Solve [tex]ty'' + 2y' + ty = 0[/tex]

with [tex]lim_{t\rightarrow0+} y = 0[/tex]

and

[tex] y(\pi) = 0[/tex]

So here's my working:

[tex]-\frac{d}{ds}[s^2Y - sy(0) - y'(0)] + 2[sY - y(0)] - Y' = 0[/tex]

[tex]-[2sY + s^2Y' - s] + 2[sY - y(0)] - Y' = 0[/tex]

Arranging terms, I get:

[tex] Y' = \frac{s-2y(0)}{s^2+1}[/tex]

and

[tex]-Y' = \frac{2y(0)-s}{s^2+1}[/tex]

[tex]L^{-1}(-Y')= L^{-1}(\frac{2y(0)}{s^2+1}) - L^{-1}(\frac{s}{s^2+1})[/tex]

[tex]ty = 2y(0)sint - cost[/tex]

[tex] y = \frac{2y(0)sint}{t} - \frac{cost}{t}[/tex]

The answer is [tex]y = \frac{sint}{t}[/tex]

What's wrong?

Thanks..

Solve [tex]ty'' + 2y' + ty = 0[/tex]

with [tex]lim_{t\rightarrow0+} y = 0[/tex]

and

[tex] y(\pi) = 0[/tex]

So here's my working:

[tex]-\frac{d}{ds}[s^2Y - sy(0) - y'(0)] + 2[sY - y(0)] - Y' = 0[/tex]

[tex]-[2sY + s^2Y' - s] + 2[sY - y(0)] - Y' = 0[/tex]

Arranging terms, I get:

[tex] Y' = \frac{s-2y(0)}{s^2+1}[/tex]

and

[tex]-Y' = \frac{2y(0)-s}{s^2+1}[/tex]

[tex]L^{-1}(-Y')= L^{-1}(\frac{2y(0)}{s^2+1}) - L^{-1}(\frac{s}{s^2+1})[/tex]

[tex]ty = 2y(0)sint - cost[/tex]

[tex] y = \frac{2y(0)sint}{t} - \frac{cost}{t}[/tex]

The answer is [tex]y = \frac{sint}{t}[/tex]

What's wrong?

Thanks..

Last edited: