What is the solution for y^{''}-5y^'+6y=3e^{2x} ?

The solution for y^{''}-5y^'+6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-3xe^{2x}

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y^{''}-5y^'+6y=3e^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 3 e^{2 x}

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 3 e^{2 x}

Solve linear ODE:

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

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

\int_{0}^{1} e^{x} - x e^{x^{2}} d x

\int \frac{x}{x - 1} d x

d er i v a t i v e ln (1 + \frac{1}{x})

\frac{d y}{d x} = \frac{( x ^{3} - 2 y )}{x}

t an g e n t 5 x^{3} + 2 x + 4, at x = 1

What is the solution for y^{''}-5y^'+6y=3e^{2x} ?
The solution for y^{''}-5y^'+6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-3xe^{2x}