What is the solution for y^{''}-10y^'-144y=0,y(0)=9,y^'(0)=58 ?

The solution for y^{''}-10y^'-144y=0,y(0)=9,y^'(0)=58 is y=5e^{18t}+4e^{-8t}

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y^{''}-10y^'-144y=0,y(0)=9,y^'(0)=58

y^{^{''}} - 10 y^{^{'}} - 144 y = 0, y (0) = 9, y^{^{'}} (0) = 58

y = 5 e^{18 t} + 4 e^{- 8 t}

Solution steps

y^{''} (t) - 10 y^{'} (t) - 144 y = 0

Solve linear ODE:

y = 5 e^{18 t} + 4 e^{- 8 t}

y = 5 e^{18 t} + 4 e^{- 8 t}

y^{^{''}} + a \cdot y^{^{'}} - b \cdot y = 0

y^{^{''}} - 10 y^{^{'}} + 6 y = 0

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 3, y^{^{'}} (0) = - 8

4 y^{^{''}} + 4 y^{^{'}} - 8 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 10, y^{^{'}} (0) = 10

What is the solution for y^{''}-10y^'-144y=0,y(0)=9,y^'(0)=58 ?
The solution for y^{''}-10y^'-144y=0,y(0)=9,y^'(0)=58 is y=5e^{18t}+4e^{-8t}