What is the solution for y^{''}+y=x^2+1 ?

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

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y^{''}+y=x^2+1

y^{^{''}} + y = x^{2} + 1

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

Solution steps

y^{''} (x) + y = x^{2} + 1

Solve linear ODE:

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

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

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