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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} - 3 + cos (x) = 0

\frac{d ^{2} y}{d x ^{2}} + y - 1 = 0, y (1) = 0

y^{^{''}} - 4 y = (x^{2} - 5) sin (2 x)

D (x) = - 12 x + 850

y^{^{''}} + b^{2} y = cos (2 t), y (0) = 1

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