What is the solution for y^{''}-5y^'-24y=0,y(0)=7,y^'(0)=-3 ?

The solution for y^{''}-5y^'-24y=0,y(0)=7,y^'(0)=-3 is y=(7-59/11)e^{8t}+59/11 e^{-3t}

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y^{''}-5y^'-24y=0,y(0)=7,y^'(0)=-3

y^{^{''}} - 5 y^{^{'}} - 24 y = 0, y (0) = 7, y^{^{'}} (0) = - 3

y = (7 - \frac{59}{11}) e^{8 t} + \frac{59}{11} e^{- 3 t}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 24 y = 0

Solve linear ODE:

y = (7 - \frac{59}{11}) e^{8 t} + \frac{59}{11} e^{- 3 t}

y = (7 - \frac{59}{11}) e^{8 t} + \frac{59}{11} e^{- 3 t}

81 y^{^{''}} + 36 y^{^{'}} + 40 y = 0, y (0) = 6, y^{^{'}} (0) = 7

2 y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 0, y (2) = 1

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

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

(10 d^{3} + d^{2} - 7 d + 2) y = 0

What is the solution for y^{''}-5y^'-24y=0,y(0)=7,y^'(0)=-3 ?
The solution for y^{''}-5y^'-24y=0,y(0)=7,y^'(0)=-3 is y=(7-59/11)e^{8t}+59/11 e^{-3t}