What is the solution for (d^2y)/(dx^2)+y=-1 ?

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

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(d^2y)/(dx^2)+y=-1

\frac{d ^{2} y}{d x ^{2}} + y = - 1

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = - 1

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + α y = 1

y^{^{''}} + 4 y = (sin (x))^{2}

y^{^{''}} + 2 y^{^{'}} + 10 y = 5

\frac{d ^{2} y}{d x ^{2}} + 60 \frac{d y}{d x} + 5000 y = 60

x^{^{''}} + x^{^{'}} + 4 = 0

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