What is the solution for y^{''}+4y=8x^2+9x ?

The solution for y^{''}+4y=8x^2+9x is y=c_{1}cos(2x)+c_{2}sin(2x)+2x^2+(9x)/4-1

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y^{''}+4y=8x^2+9x

y^{^{''}} + 4 y = 8 x^{2} + 9 x

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{9 x}{4} - 1

Solution steps

y^{''} (x) + 4 y = 8 x^{2} + 9 x

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{9 x}{4} - 1

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{9 x}{4} - 1

What is the solution for y^{''}+4y=8x^2+9x ?
The solution for y^{''}+4y=8x^2+9x is y=c_{1}cos(2x)+c_{2}sin(2x)+2x^2+(9x)/4-1