What is the solution for (d^2y)/(dx^2)+4y=8 ?

The solution for (d^2y)/(dx^2)+4y=8 is y=c_{1}cos(2x)+c_{2}sin(2x)+2

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(d^2y)/(dx^2)+4y=8

\frac{d ^{2} y}{d x ^{2}} + 4 y = 8

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = 8

Solve linear ODE:

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

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

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

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 3

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

y^{^{''}} - 9 y^{^{'}} + 14 y = 30 t - 34

y^{^{''}} + y = 6 sin (2 t), y (0) = 3, y^{^{'}} (0) = 1

What is the solution for (d^2y)/(dx^2)+4y=8 ?
The solution for (d^2y)/(dx^2)+4y=8 is y=c_{1}cos(2x)+c_{2}sin(2x)+2