What is the solution for (d^2y)/(dx^2)+y=0,y=cos(x)+sin(x) ?

The solution for (d^2y)/(dx^2)+y=0,y=cos(x)+sin(x) is y=c_{1}cos(x)+c_{2}sin(x)

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(d^2y)/(dx^2)+y=0,y=cos(x)+sin(x)

\frac{d ^{2} y}{d x ^{2}} + y = 0, y = cos (x) + sin (x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 0

Solve linear ODE:

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

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

64 y^{^{''}} + 96 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 8

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 16 y = 0

y^{^{''}} + \frac{32}{13} y^{^{'}} + 32 y = 0

0.2 y^{^{''}} + 14 y^{^{'}} + \frac{1}{0.004} y = 0, y (0) = 0

2 \frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 3 y = 0

What is the solution for (d^2y)/(dx^2)+y=0,y=cos(x)+sin(x) ?
The solution for (d^2y)/(dx^2)+y=0,y=cos(x)+sin(x) is y=c_{1}cos(x)+c_{2}sin(x)