What is the solution for y^{''}-3y^'+2y=6e^x-2xe^{2x}+2 ?

The solution for y^{''}-3y^'+2y=6e^x-2xe^{2x}+2 is y=c_{1}e^{2x}+c_{2}e^x-6xe^x-e^{2x}x^2+2xe^{2x}+1

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y^{''}-3y^'+2y=6e^x-2xe^{2x}+2

y^{^{''}} - 3 y^{^{'}} + 2 y = 6 e^{x} - 2 x e^{2 x} + 2

y = c_{1} e^{2 x} + c_{2} e^{x} - 6 x e^{x} - e^{2 x} x^{2} + 2 x e^{2 x} + 1

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 6 e^{x} - 2 x e^{2 x} + 2

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - 6 x e^{x} - e^{2 x} x^{2} + 2 x e^{2 x} + 1

y = c_{1} e^{2 x} + c_{2} e^{x} - 6 x e^{x} - e^{2 x} x^{2} + 2 x e^{2 x} + 1

y^{^{''}} + 3 y^{^{'}} - 6 y = x e^{2 x}

y^{^{''}} + 2 y^{^{'}} = x + 1

x^{^{''}} + x = 8 cos (6 t)

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

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 cos (9 t)

What is the solution for y^{''}-3y^'+2y=6e^x-2xe^{2x}+2 ?
The solution for y^{''}-3y^'+2y=6e^x-2xe^{2x}+2 is y=c_{1}e^{2x}+c_{2}e^x-6xe^x-e^{2x}x^2+2xe^{2x}+1