What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=4e^{2x} ?

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

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=4e^{2x}

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{''}} - 8 y = 2

y^{^{''}} - y = 2.9 cos (t), y (0) = 0, y^{^{'}} (0) = 2.9

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 5 y = e^{x}

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

y^{^{''}} + 8 y^{^{'}} + 15 y = - 6 cos (5 x)

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