What is the solution for y^{''}+y=0,y^'=5,y(0)=9 ?

The solution for y^{''}+y=0,y^'=5,y(0)=9 is y=9cos(t)+5sin(t)

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

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

y = 9 cos (t) + 5 sin (t)

Solution steps

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

Solve linear ODE:

y = 9 cos (t) + 5 sin (t)

y = 9 cos (t) + 5 sin (t)

y^{^{''}} = 7 y^{^{'}} + 4 y

y^{^{''}} + 0.05 y^{^{'}} + 25 y = 0

2 \cdot y^{^{''}} + 4 \cdot y^{^{'}} + 8 y = 0

5 y^{^{''}} + 18 y^{^{'}} + 9 y = 0, y (0) = 17.4

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (1) = 3

What is the solution for y^{''}+y=0,y^'=5,y(0)=9 ?
The solution for y^{''}+y=0,y^'=5,y(0)=9 is y=9cos(t)+5sin(t)