Laplace

Calculus Level 3

Find the function $y(t)$ that complies with:

$t$ $\frac{d^2y}{dt^2}$ $-$ $t$ $\frac{dy}{dt}$ $+$ $y$ $=$ $0$

With $y(0)=0$ and $y'(0)=1$

y(t)=t y(t)=kt y(t)=e^t y(t)=log(t)

1 solution

Henry U
Dec 1, 2018

Only $y(t)=t$ and $y(t)=kt$ satisfy $y(0)=0$ and only $y(t)=t$ and $y(t)=e^t$ satisfy $y^\prime(0)=1$ , so the only possible answer is $\boxed{y(t)=t}$ .

Laplace

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