What is the solution for y^{''}+2y=4^3+5x^2-x+7 ?

The solution for y^{''}+2y=4^3+5x^2-x+7 is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+(5x^2)/2-x/2+33

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y^{''}+2y=4^3+5x^2-x+7

y^{^{''}} + 2 y = 4^{3} + 5 x^{2} - x + 7

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{5 x ^{2}}{2} - \frac{x}{2} + 33

Solution steps

y^{''} (x) + 2 y = 4^{3} + 5 x^{2} - x + 7

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{5 x ^{2}}{2} - \frac{x}{2} + 33

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{5 x ^{2}}{2} - \frac{x}{2} + 33

What is the solution for y^{''}+2y=4^3+5x^2-x+7 ?
The solution for y^{''}+2y=4^3+5x^2-x+7 is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)+(5x^2)/2-x/2+33