What is the solution for (d^2y)/(dx^2)+y=x^2+2 ?

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

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(d^2y)/(dx^2)+y=x^2+2

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

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

Solution steps

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

\int \frac{1}{( t + 4 ) ( t - 1 )} d t

(x y - y^{2}) d x - x^{2} d y = 0

\frac{\partial}{\partial x} (- 5 y^{2} sin (x y^{2}))

\frac{\partial}{\partial y} (20 (y - x^{2}))

x \to 1 lim (\frac{x ^{2} + 1}{x + 5})

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