What is the solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y ?

The solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y is y=c_{1}e^{sqrt(3/2)t}+c_{2}e^{-sqrt(3/2)t}

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y^{''}+2y^'+y=5y-y^{''}+2y^'-y

y^{^{''}} + 2 y^{^{'}} + y = 5 y - y^{^{''}} + 2 y^{^{'}} - y

y = c_{1} e^{\frac{3}{2} t} + c_{2} e^{- \frac{3}{2} t}

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 5 y - y^{''} (t) + 2 y^{'} (t) - y

Solve linear ODE:

y = c_{1} e^{\frac{3}{2} t} + c_{2} e^{- \frac{3}{2} t}

y = c_{1} e^{\frac{3}{2} t} + c_{2} e^{- \frac{3}{2} t}

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = 0

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

x^{^{''}} + 2 x^{^{'}} - 3 x = 0

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = - 1, y^{^{'}} (0) = - 3

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0, y (0) = - 1, y^{^{'}} (0) = - 4

What is the solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y ?
The solution for y^{''}+2y^'+y=5y-y^{''}+2y^'-y is y=c_{1}e^{sqrt(3/2)t}+c_{2}e^{-sqrt(3/2)t}