What is the solution for 3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=-5/3 ?

The solution for 3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=-5/3 is y=(4-9/13)e^{t/3}+9/13 e^{-4t}

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3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=-5/3

3 y^{^{''}} + 11 y^{^{'}} - 4 y = 0, y (0) = 4, y^{^{'}} (0) = - \frac{5}{3}

y = (4 - \frac{9}{13}) e^{\frac{t}{3}} + \frac{9}{13} e^{- 4 t}

Solution steps

3 y^{''} (t) + 11 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = (4 - \frac{9}{13}) e^{\frac{t}{3}} + \frac{9}{13} e^{- 4 t}

y = (4 - \frac{9}{13}) e^{\frac{t}{3}} + \frac{9}{13} e^{- 4 t}

y^{^{''}} + 20 y = 0

(D^{2} + 4 D + 5) y = 0

y^{^{''}} + 2 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 6

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 5

y^{^{''}} - 16 y^{^{'}} + 68 y = 0

What is the solution for 3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=-5/3 ?
The solution for 3y^{''}+11y^'-4y=0,y(0)=4,y^'(0)=-5/3 is y=(4-9/13)e^{t/3}+9/13 e^{-4t}