What is the solution for y^{''}+15y^'+50y=0,y(0)=12,y^'(0)=-105 ?

The solution for y^{''}+15y^'+50y=0,y(0)=12,y^'(0)=-105 is y=3e^{-5t}+9e^{-10t}

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y^{''}+15y^'+50y=0,y(0)=12,y^'(0)=-105

y^{^{''}} + 15 y^{^{'}} + 50 y = 0, y (0) = 12, y^{^{'}} (0) = - 105

y = 3 e^{- 5 t} + 9 e^{- 10 t}

Solution steps

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

Solve linear ODE:

y = 3 e^{- 5 t} + 9 e^{- 10 t}

y = 3 e^{- 5 t} + 9 e^{- 10 t}

What is the solution for y^{''}+15y^'+50y=0,y(0)=12,y^'(0)=-105 ?
The solution for y^{''}+15y^'+50y=0,y(0)=12,y^'(0)=-105 is y=3e^{-5t}+9e^{-10t}