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

3 y^{^{''}} + 8 y^{^{'}} + 4 y = e^{- 2 x}

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2 x} + 2 sin (x)

y^{^{''}} + 2 y^{^{'}} - 2 y = x^{2} - e^{x} cos (2 x)

(D^{4} + 2 D^{3} - 3 D^{2}) y = 3 e^{2 x} + 4 sin (x)

y^{^{'''}} - 4 y^{^{''}} + y^{^{'}} + 6 y = 3 e^{4 t}

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