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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} = 49 y

\frac{d}{d x} (6^{4} x^{3} + x^{5} - 180 4 x^{2})

\frac{d}{d x} (\frac{- e ^{- x} x - e ^{- x}}{x ^{2}})

\int_{- 7}^{7} (1 + 49 - x^{2}) d x

\frac{d y}{d x} = \frac{x ^{2} + 2 y ^{2}}{x y}

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