What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+4y=1 ?

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

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(d^2y)/(dx^2)-4(dy)/(dx)+4y=1

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 1

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 1

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = 4 sin (x)

y^{^{''}} - 2 y - 24 = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 t

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 24 e^{3 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 sin (t) - 2 cos (t)

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