What is the solution for y^{''}-4y=3e^{2t} ?

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

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y^{''}-4y=3e^{2t}

y^{^{''}} - 4 y = 3 e^{2 t}

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

Solution steps

y^{''} (t) - 4 y = 3 e^{2 t}

Solve linear ODE:

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

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

9 y^{^{''}} + 7 y^{^{'}} - y = 24

y^{^{''}} + 16 y = 8 x + 8 sin (x)

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 4 e^{- 2 x}

y^{^{''}} - 3 y^{^{'}} = x^{2} - 1

9 y^{^{''}} + 24 y^{^{'}} + 16 y = 8 e^{x}

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