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

The solution for y^{''}-5y^'+6y=xe^x is y=c_{1}e^{3x}+c_{2}e^{2x}+(e^xx)/2+3/4 e^x

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y^{''}-5y^'+6y=xe^x

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

\int \frac{e ^{6 x}}{e ^{6 x} - 3 e ^{- 6 x}} d x

\int \frac{8 y}{x} d x

x \to \infty lim (\frac{3.4}{0.1 + 33.9 e ^{- 0.5678 x}})

t^{3} 1 (t)

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})

What is the solution for y^{''}-5y^'+6y=xe^x ?
The solution for y^{''}-5y^'+6y=xe^x is y=c_{1}e^{3x}+c_{2}e^{2x}+(e^xx)/2+3/4 e^x