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# LT for ODE with Non-constant Coefficients

DIFFEQ-X42LJD

Consider the equation $ty''+y'+ty=0$ with $y(0)$ well-defined.

The Laplace Transform of $y(t)$, denoted by $Y(s)$, is:

A

$[tsy(0)+ty'(0)+y(0)]/(ts^2+s+t)$

B

$-s/(1+s^2)$

C

$C(1+s^2)^{-1/2}, C\in\mathbb{R}$

D

$C(1+s^2)^{1/2}, C\in\mathbb{R}$

E

$-Cs/(1+s^2), C\in\mathbb{R}$