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

The solution for y^{''}+y=0,y^'(0)=-5 is y=c_{1}cos(t)-5sin(t)

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

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

y = c_{1} cos (t) - 5 sin (t)

Solution steps

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

Solve linear ODE:

y = c_{1} cos (t) - 5 sin (t)

y = c_{1} cos (t) - 5 sin (t)

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 3

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 1

6 y^{^{''}} - y^{^{'}} + 2 y = 0

What is the solution for y^{''}+y=0,y^'(0)=-5 ?
The solution for y^{''}+y=0,y^'(0)=-5 is y=c_{1}cos(t)-5sin(t)