What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+4y=2x ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)+4y=2x is y=c_{1}e^{2x}+c_{2}xe^{2x}+x/2+1/2

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(d^2y)/(dx^2)-4(dy)/(dx)+4y=2x

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 2 x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 2 x

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 4 cos (2 x), y^{^{'}} (\frac{π}{2}) = 0, y (0) = 1

x^{^{''}} + 9 x = sin (t)

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{(2 t)}

y^{^{''}} + 2 y^{^{'}} + 10 y = 10

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{x}

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