What is the solution for y^{''}-4y=-12e^{-2x}+15cos(x)+8x ?

The solution for y^{''}-4y=-12e^{-2x}+15cos(x)+8x is y=c_{1}e^{2x}+c_{2}e^{-2x}+3xe^{-2x}-3cos(x)-2x

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y^{''}-4y=-12e^{-2x}+15cos(x)+8x

y^{^{''}} - 4 y = - 12 e^{- 2 x} + 15 cos (x) + 8 x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + 3 x e^{- 2 x} - 3 cos (x) - 2 x

Solution steps

y^{''} (x) - 4 y = - 12 e^{- 2 x} + 15 cos (x) + 8 x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + 3 x e^{- 2 x} - 3 cos (x) - 2 x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + 3 x e^{- 2 x} - 3 cos (x) - 2 x

What is the solution for y^{''}-4y=-12e^{-2x}+15cos(x)+8x ?
The solution for y^{''}-4y=-12e^{-2x}+15cos(x)+8x is y=c_{1}e^{2x}+c_{2}e^{-2x}+3xe^{-2x}-3cos(x)-2x