What is the solution for y^{''}+3y^'+2y=t ?

The solution for y^{''}+3y^'+2y=t is y=c_{1}e^{-t}+c_{2}e^{-2t}+t/2-3/4

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y^{''}+3y^'+2y=t

y^{^{''}} + 3 y^{^{'}} + 2 y = t

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{t}{2} - \frac{3}{4}

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = t

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{t}{2} - \frac{3}{4}

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{t}{2} - \frac{3}{4}

f (x) = 3 (x)^{2} - 2 (x)

\frac{d y}{d x} = 4 - \frac{5 y}{300 - 3 x}

\int \frac{1}{x ^{2}} d x

x \to 1 lim (5 - 2 x)

x \to - π lim (x + 4)

What is the solution for y^{''}+3y^'+2y=t ?
The solution for y^{''}+3y^'+2y=t is y=c_{1}e^{-t}+c_{2}e^{-2t}+t/2-3/4