What is the solution for y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42 ?

The solution for y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42 is y=7e^{-3t}+3e^{-7t}

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y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42

y^{^{''}} + 10 y^{^{'}} + 21 y = 0, y (0) = 10, y^{^{'}} (0) = - 42

y = 7 e^{- 3 t} + 3 e^{- 7 t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 21 y = 0

Solve linear ODE:

y = 7 e^{- 3 t} + 3 e^{- 7 t}

y = 7 e^{- 3 t} + 3 e^{- 7 t}

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What is the solution for y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42 ?
The solution for y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42 is y=7e^{-3t}+3e^{-7t}