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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 9 y = g (t), y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 16 y = sinh (x)

4 y^{^{''}} - 6 y^{^{'}} + 2 y = 24 e^{- x} - 10 sin (x)

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 5 e^{- x}

y^{^{''}} - 16 y^{^{'}} + 64 y = \frac{2 e ^{8 x}}{3 x}

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