What is the solution for 2y^{''}+3y-2y=6x^2+5x-8 ?

The solution for 2y^{''}+3y-2y=6x^2+5x-8 is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+6x^2+5x-32

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2y^{''}+3y-2y=6x^2+5x-8

2 y^{^{''}} + 3 y - 2 y = 6 x^{2} + 5 x - 8

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 6 x^{2} + 5 x - 32

Solution steps

2 y^{''} (x) + 3 y - 2 y = 6 x^{2} + 5 x - 8

Solve linear ODE:

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 6 x^{2} + 5 x - 32

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 6 x^{2} + 5 x - 32

What is the solution for 2y^{''}+3y-2y=6x^2+5x-8 ?
The solution for 2y^{''}+3y-2y=6x^2+5x-8 is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+6x^2+5x-32