What is the solution for y^{''}-2y^'+y=2000x^2-150e^x ?

The solution for y^{''}-2y^'+y=2000x^2-150e^x is y=c_{1}e^x+c_{2}xe^x+2000x^2+8000x+12000-75x^2e^x

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y^{''}-2y^'+y=2000x^2-150e^x

y^{^{''}} - 2 y^{^{'}} + y = 2000 x^{2} - 150 e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 2000 x^{2} - 150 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

What is the solution for y^{''}-2y^'+y=2000x^2-150e^x ?
The solution for y^{''}-2y^'+y=2000x^2-150e^x is y=c_{1}e^x+c_{2}xe^x+2000x^2+8000x+12000-75x^2e^x