What is the solution for y^{''}-2y^'=6e^{2x} ?

The solution for y^{''}-2y^'=6e^{2x} is y=c_{1}e^{2x}+c_{2}+3xe^{2x}

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y^{''}-2y^'=6e^{2x}

y^{^{''}} - 2 y^{^{'}} = 6 e^{2 x}

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

Solution steps

y^{''} (x) - 2 y^{'} (x) = 6 e^{2 x}

Solve linear ODE:

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

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

\int \frac{9 x ^{2} + 6 x + 9}{x ^{3} - 1} d x

e^{2 t} sin (2 t j)

y = c cos (t) + t^{2} sin (t)

\frac{\partial}{\partial y} (x + 2 y + 1)

6 cos (4 t - 1)

What is the solution for y^{''}-2y^'=6e^{2x} ?
The solution for y^{''}-2y^'=6e^{2x} is y=c_{1}e^{2x}+c_{2}+3xe^{2x}