What is the solution for y^{''}+15y^'+50y=0,y(0)=8,y^'(0)=-55 ?

The solution for y^{''}+15y^'+50y=0,y(0)=8,y^'(0)=-55 is y=5e^{-5t}+3e^{-10t}

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

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

y = 5 e^{- 5 t} + 3 e^{- 10 t}

Solution steps

y^{''} (t) + 15 y^{'} (t) + 50 y = 0

Solve linear ODE:

y = 5 e^{- 5 t} + 3 e^{- 10 t}

y = 5 e^{- 5 t} + 3 e^{- 10 t}

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

y^{^{''}} - 14 y^{^{'}} + 49 y = 0, y (0) = - 6, y^{^{'}} (0) = 0

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

\frac{1}{4} y^{^{''}} + y = 0

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

What is the solution for y^{''}+15y^'+50y=0,y(0)=8,y^'(0)=-55 ?
The solution for y^{''}+15y^'+50y=0,y(0)=8,y^'(0)=-55 is y=5e^{-5t}+3e^{-10t}