What is the solution for 3y^{''}+38y^'+80y=0,y(0)=3,y^'(0)=7 ?

The solution for 3y^{''}+38y^'+80y=0,y(0)=3,y^'(0)=7 is y=(3+45/22)e^{-(8t)/3}-45/22 e^{-10t}

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3y^{''}+38y^'+80y=0,y(0)=3,y^'(0)=7

3 y^{^{''}} + 38 y^{^{'}} + 80 y = 0, y (0) = 3, y^{^{'}} (0) = 7

y = (3 + \frac{45}{22}) e^{- \frac{8 t}{3}} - \frac{45}{22} e^{- 10 t}

Solution steps

3 y^{''} (t) + 38 y^{'} (t) + 80 y = 0

Solve linear ODE:

y = (3 + \frac{45}{22}) e^{- \frac{8 t}{3}} - \frac{45}{22} e^{- 10 t}

y = (3 + \frac{45}{22}) e^{- \frac{8 t}{3}} - \frac{45}{22} e^{- 10 t}

a x^{^{''}} + b x^{^{'}} + c x = 0

y^{^{''}} - 361 y = 0

3 y^{^{''}} - 2 y^{^{'}} + 6 y = 0

y^{^{'''}} + 36 y^{^{'}} = 0, y (0) = 1

y^{^{''}} - y^{^{'}} = - 10 y

What is the solution for 3y^{''}+38y^'+80y=0,y(0)=3,y^'(0)=7 ?
The solution for 3y^{''}+38y^'+80y=0,y(0)=3,y^'(0)=7 is y=(3+45/22)e^{-(8t)/3}-45/22 e^{-10t}