What is the solution for y^{''}+81y=0,y(0)=4,y^'(0)=1 ?

The solution for y^{''}+81y=0,y(0)=4,y^'(0)=1 is y=4cos(9t)+1/9 sin(9t)

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y^{''}+81y=0,y(0)=4,y^'(0)=1

y^{^{''}} + 81 y = 0, y (0) = 4, y^{^{'}} (0) = 1

y = 4 cos (9 t) + \frac{1}{9} sin (9 t)

Solution steps

y^{''} (t) + 81 y = 0

Solve linear ODE:

y = 4 cos (9 t) + \frac{1}{9} sin (9 t)

y = 4 cos (9 t) + \frac{1}{9} sin (9 t)

4 y^{^{''}} - 12 y^{^{'}} + 10 y = 0

y^{^{''}} + 5 y^{^{'}} + 13 y = 0

y^{^{''}} + 10 y^{^{'}} + 23 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 15 y^{^{'}} + 50 y = 0, y (0) = 8, y^{^{'}} (0) = - 55

y^{^{''}} + 5 y^{^{'}} + 25 y = 0

What is the solution for y^{''}+81y=0,y(0)=4,y^'(0)=1 ?
The solution for y^{''}+81y=0,y(0)=4,y^'(0)=1 is y=4cos(9t)+1/9 sin(9t)