What is the solution for y^{''}+y=0,y^{''}(0)=0,y(0)=1 ?

The solution for y^{''}+y=0,y^{''}(0)=0,y(0)=1 is y=c_{2}sin(t)

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y^{''}+y=0,y^{''}(0)=0,y(0)=1

y^{^{''}} + y = 0, y^{^{''}} (0) = 0, y (0) = 1

y = c_{2} sin (t)

Solution steps

y^{''} (t) + y = 0

Solve linear ODE:

y = c_{2} sin (t)

y = c_{2} sin (t)

4 y^{^{''}} - 4 y + 5 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 1

y^{^{''}} - 10 y^{^{'}} - 16 y = 0

y^{^{'}} + y = y^{^{''}}

\frac{5}{6} y^{^{''}} + 10 y^{^{'}} + 60 y = 0, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 0

What is the solution for y^{''}+y=0,y^{''}(0)=0,y(0)=1 ?
The solution for y^{''}+y=0,y^{''}(0)=0,y(0)=1 is y=c_{2}sin(t)