What is the solution for y^{''}+81y=0,y(0)=3,y^'(0)=8 ?

The solution for y^{''}+81y=0,y(0)=3,y^'(0)=8 is y=3cos(9t)+8/9 sin(9t)

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y^{''}+81y=0,y(0)=3,y^'(0)=8

y^{^{''}} + 81 y = 0, y (0) = 3, y^{^{'}} (0) = 8

y = 3 cos (9 t) + \frac{8}{9} sin (9 t)

Solution steps

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

Solve linear ODE:

y = 3 cos (9 t) + \frac{8}{9} sin (9 t)

y = 3 cos (9 t) + \frac{8}{9} sin (9 t)

14 y^{^{''}} - 15 y^{^{'}} + y = 0, y (0) = 14, y^{^{'}} (0) = \frac{1}{14}

5 y^{^{''}} - 7 y^{^{'}} - 3 y = 0

y^{^{''}} - 6 y^{^{'}} + 18 y = 0, y (0) = 0, y^{^{'}} (0) = 6

y^{^{''}} + 2 y^{^{'}} + y = 0, y^{1} (0) = x^{e} - x

y^{^{''}} + \frac{64}{5} y^{^{'}} + 64 y = 0

What is the solution for y^{''}+81y=0,y(0)=3,y^'(0)=8 ?
The solution for y^{''}+81y=0,y(0)=3,y^'(0)=8 is y=3cos(9t)+8/9 sin(9t)