What is the solution for y^{''}-4y^'+4y=-7x+4x ?

The solution for y^{''}-4y^'+4y=-7x+4x is y=c_{1}e^{2x}+c_{2}xe^{2x}-(3x)/4-3/4

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y^{''}-4y^'+4y=-7x+4x

y^{^{''}} - 4 y^{^{'}} + 4 y = - 7 x + 4 x

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = - 7 x + 4 x

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + a \frac{d y}{d x} = g

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

9 y^{^{''}} - 16 y = sin (x)

y^{^{'''}} + y^{^{'}} - 10 y = 29 e^{4 x}

f^{^{''}} (x) + 3 f^{^{'}} (x) + 2 f (x) = 2, f (0) = 3, f^{^{'}} (0) = 5

What is the solution for y^{''}-4y^'+4y=-7x+4x ?
The solution for y^{''}-4y^'+4y=-7x+4x is y=c_{1}e^{2x}+c_{2}xe^{2x}-(3x)/4-3/4