What is the solution for y^{''}+4y^'-60y=0,y(0)=3,y^'(0)=2 ?

The solution for y^{''}+4y^'-60y=0,y(0)=3,y^'(0)=2 is y=2e^{6t}+e^{-10t}

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y^{''}+4y^'-60y=0,y(0)=3,y^'(0)=2

y^{^{''}} + 4 y^{^{'}} - 60 y = 0, y (0) = 3, y^{^{'}} (0) = 2

y = 2 e^{6 t} + e^{- 10 t}

Solution steps

y^{''} (t) + 4 y^{'} (t) - 60 y = 0

Solve linear ODE:

y = 2 e^{6 t} + e^{- 10 t}

y = 2 e^{6 t} + e^{- 10 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 4

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 12, y^{^{'}} (0) = - 52

y^{^{''}} + y = 0, y (0) = 13, y (0) = 29

3 (\frac{d ^{2} y}{d x ^{2}}) + 19 (\frac{d y}{d x}) - 14 y = 0

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

What is the solution for y^{''}+4y^'-60y=0,y(0)=3,y^'(0)=2 ?
The solution for y^{''}+4y^'-60y=0,y(0)=3,y^'(0)=2 is y=2e^{6t}+e^{-10t}