What is the solution for y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1 ?

The solution for y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1 is y=-e^{-7t}-6e^{-7t}t

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y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (0) = - 1, y^{^{'}} (0) = 1

y = - e^{- 7 t} - 6 e^{- 7 t} t

Solution steps

y^{''} (t) + 14 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = - e^{- 7 t} - 6 e^{- 7 t} t

y = - e^{- 7 t} - 6 e^{- 7 t} t

What is the solution for y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1 ?
The solution for y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1 is y=-e^{-7t}-6e^{-7t}t