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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int 9 x^{2} - 4 x d x

\frac{\partial}{\partial x} (1 + ln (x))

s (t) = \frac{t ^{2} + 40 t}{5}

\frac{\partial}{\partial x} (e^{(x^{2} - y^{2})})

(36 - x^{2}) \frac{d y}{d x} = 1

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