What is the solution for 4y^{''}+22y^'+18y=0,y(0)=3,y^'(0)=0 ?

The solution for 4y^{''}+22y^'+18y=0,y(0)=3,y^'(0)=0 is y=(3+6/7)e^{-t}-6/7 e^{-(9t)/2}

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4y^{''}+22y^'+18y=0,y(0)=3,y^'(0)=0

4 y^{^{''}} + 22 y^{^{'}} + 18 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y = (3 + \frac{6}{7}) e^{- t} - \frac{6}{7} e^{- \frac{9 t}{2}}

Solution steps

4 y^{''} (t) + 22 y^{'} (t) + 18 y = 0

Solve linear ODE:

y = (3 + \frac{6}{7}) e^{- t} - \frac{6}{7} e^{- \frac{9 t}{2}}

y = (3 + \frac{6}{7}) e^{- t} - \frac{6}{7} e^{- \frac{9 t}{2}}

2 y^{^{''}} - 5 y - 3 y = 0

y^{^{''}} + 10.5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 12 y = 0

y^{^{''}} - 4 y = 0, y (0) = 0

y^{^{''''}} + 4 y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + y = 0

What is the solution for 4y^{''}+22y^'+18y=0,y(0)=3,y^'(0)=0 ?
The solution for 4y^{''}+22y^'+18y=0,y(0)=3,y^'(0)=0 is y=(3+6/7)e^{-t}-6/7 e^{-(9t)/2}