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}

f (x) = 2 x^{3} - 8 x, (- 2, 0)

\int ((4 x + 3) \cdot (2 x^{2} + 3 x)^{3}) d x

f (x) = x \cdot sin (x)

\frac{d}{d x} (\frac{8 x ^{2} + 2 x + 8}{x})

x \to + 0 lim (x sin (\frac{3}{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