What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9 ?

The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9 is y=c_{1}e^{2x}+c_{2}e^x+(x^2)/2+(11x)/2+49/4

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}

y^{^{''}} + 4 y^{^{'}} + 4 y = 1

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

y^{^{''}} + 4 y^{^{'}} = tan (2 x)

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

y^{^{''}} - 4 y^{^{'}} + 5 y = \frac{2 e ^{x}}{sin ( x )}

What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9 ?
The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9 is y=c_{1}e^{2x}+c_{2}e^x+(x^2)/2+(11x)/2+49/4