What is the solution for y^{''}+y^'-30y=0,y(0)=1,y^'(0)=38 ?

The solution for y^{''}+y^'-30y=0,y(0)=1,y^'(0)=38 is y=4e^{5t}-3e^{-6t}

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y^{''}+y^'-30y=0,y(0)=1,y^'(0)=38

y^{^{''}} + y^{^{'}} - 30 y = 0, y (0) = 1, y^{^{'}} (0) = 38

y = 4 e^{5 t} - 3 e^{- 6 t}

Solution steps

y^{''} (t) + y^{'} (t) - 30 y = 0

Solve linear ODE:

y = 4 e^{5 t} - 3 e^{- 6 t}

y = 4 e^{5 t} - 3 e^{- 6 t}

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = - 13

y^{^{''}} - 9 y^{^{'}} + 6 y = 0

16 y^{^{''}} + 522.67 y = 0

\frac{d ^{2} y}{d t ^{2}} + 64 y = 0

What is the solution for y^{''}+y^'-30y=0,y(0)=1,y^'(0)=38 ?
The solution for y^{''}+y^'-30y=0,y(0)=1,y^'(0)=38 is y=4e^{5t}-3e^{-6t}