What is the solution for y^{''}-2y^'-15y=0,y(0)=1,y^'(0)=37 ?

The solution for y^{''}-2y^'-15y=0,y(0)=1,y^'(0)=37 is y=5e^{5t}-4e^{-3t}

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y^{''}-2y^'-15y=0,y(0)=1,y^'(0)=37

y^{^{''}} - 2 y^{^{'}} - 15 y = 0, y (0) = 1, y^{^{'}} (0) = 37

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

Solution steps

y^{''} (t) - 2 y^{'} (t) - 15 y = 0

Solve linear ODE:

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

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

2 u^{^{''}} + \frac{3}{5} u^{^{'}} + 30 H (t) = 0

49 y^{^{''}} - 112 y^{^{'}} + 64 y = 0

- \frac{d ^{2} y}{d x ^{2}} + 400 y = 0

y^{^{''}} + 4 y - 5 y = 0

y^{^{''}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 6

What is the solution for y^{''}-2y^'-15y=0,y(0)=1,y^'(0)=37 ?
The solution for y^{''}-2y^'-15y=0,y(0)=1,y^'(0)=37 is y=5e^{5t}-4e^{-3t}