What is the solution for (d^2y)/(dx^2)+y=0,y=1,y^'=0 ?

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

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(d^2y)/(dx^2)+y=0,y=1,y^'=0

\frac{d ^{2} y}{d x ^{2}} + y = 0, y = 1, y^{^{'}} = 0

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

Solution steps

y^{''} (x) + y = 0

Solve linear ODE:

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

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

y^{^{'''}} + 3.2 y^{^{''}} + 4.81 y^{^{'}} = 0

3 y^{^{''}} + 27 y^{^{'}} + 42 y = 0

y^{^{''}} - 16 y = 0, y (0) = 4

21 y^{^{''''}} + 187 y^{^{''}} + 400 y = 0

25 y^{^{''}} - 16 y = 0

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