What is the solution for y^{''}+y=0,y(0)=-1,y^'(0)=-5 ?

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

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

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

y = - cos (t) - 5 sin (t)

Solution steps

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

Solve linear ODE:

y = - cos (t) - 5 sin (t)

y = - cos (t) - 5 sin (t)

y^{^{''''}} - 12 y^{^{'''}} + 36 y^{^{''}} = 0

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 0

7 y^{^{''}} + 7 y = 0

y^{^{''}} - 6 y^{^{'}} - 16 y = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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