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

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

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + 3 e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 3 e^{2 x}

y = c_{1} e^{x} + c_{2} x e^{x} + 3 e^{2 x}

y^{^{''}} - 18 y^{^{'}} + 81 y = (x + 1) e^{x}

4 y^{^{''}} + y = 2 sec (\frac{x}{2})

y^{^{''}} + y^{^{'}} - 12 y = 2 x

y^{^{''}} + 9 y = 9

y^{^{''}} - 5 y^{^{'}} - 6 y = 3 cos (x) + 19 sin (x)

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