What is the solution for y^{''}+9y=9x^2+9x+11 ?

The solution for y^{''}+9y=9x^2+9x+11 is y=c_{1}cos(3x)+c_{2}sin(3x)+x^2+x+1

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y^{''}+9y=9x^2+9x+11

y^{^{''}} + 9 y = 9 x^{2} + 9 x + 11

y = c_{1} cos (3 x) + c_{2} sin (3 x) + x^{2} + x + 1

Solution steps

y^{''} (x) + 9 y = 9 x^{2} + 9 x + 11

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + x^{2} + x + 1

y = c_{1} cos (3 x) + c_{2} sin (3 x) + x^{2} + x + 1

x \frac{d y}{d x} + y ln (x) - y = y ln (y)

\frac{\partial}{\partial y} (\frac{1}{x ^{2} yz})

\frac{d y}{d t} - \frac{5}{t} y = t^{5}

\frac{d}{d x} (\frac{- 1 x + 1 + x}{x ^{2} - 1})

\frac{d}{d x} (1 - 5 cos (x))

What is the solution for y^{''}+9y=9x^2+9x+11 ?
The solution for y^{''}+9y=9x^2+9x+11 is y=c_{1}cos(3x)+c_{2}sin(3x)+x^2+x+1