What is the solution for 9y^{''}-30y^'-24y=0,y(0)=0,y^'(0)=1 ?

The solution for 9y^{''}-30y^'-24y=0,y(0)=0,y^'(0)=1 is y= 3/14 e^{4t}-3/14 e^{-(2t)/3}

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9y^{''}-30y^'-24y=0,y(0)=0,y^'(0)=1

9 y^{^{''}} - 30 y^{^{'}} - 24 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{3}{14} e^{4 t} - \frac{3}{14} e^{- \frac{2 t}{3}}

Solution steps

9 y^{''} (t) - 30 y^{'} (t) - 24 y = 0

Solve linear ODE:

y = \frac{3}{14} e^{4 t} - \frac{3}{14} e^{- \frac{2 t}{3}}

y = \frac{3}{14} e^{4 t} - \frac{3}{14} e^{- \frac{2 t}{3}}

y^{^{''}} + 5 y^{^{'}} + 7 y = 0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = 0

x^{^{''}} + 10 x^{^{'}} + 15 x = 0

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

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{''}} (0) = 13

What is the solution for 9y^{''}-30y^'-24y=0,y(0)=0,y^'(0)=1 ?
The solution for 9y^{''}-30y^'-24y=0,y(0)=0,y^'(0)=1 is y= 3/14 e^{4t}-3/14 e^{-(2t)/3}