What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=xe^x ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=xe^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(e^xx)/4+1/4 e^x

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(d^2y)/(dx^2)-6(dy)/(dx)+9y=xe^x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = x e^{x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = x e^{x}

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{'}} = csc (t)

y^{^{'''}} + 4 y^{^{'}} = sin (x) cos (x)

y^{^{'''}} + y^{^{''}} = 3 e^{- x} + x

y^{^{''}} + 25 y = 9 sec (5 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = e^{2 x}

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=xe^x ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=xe^x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(e^xx)/4+1/4 e^x