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

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

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

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

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 x e^{2 x} + x + \frac{3}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 x e^{2 x} + x + \frac{3}{2}

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 x e^{2 x} + x + \frac{3}{2}

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 cos (x)

y^{^{''}} + 4 y = 3 sin (x) + cos (3 x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 3 - 2 x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 x + 18

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 5 e^{2 x}

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