What is the solution for y^{''}-y^'-72y=0,y(1)=e^{-8x} ?

The solution for y^{''}-y^'-72y=0,y(1)=e^{-8x} is y=c_{1}e^{9x}+c_{2}e^{-8x}

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y^{''}-y^'-72y=0,y(1)=e^{-8x}

y^{^{''}} - y^{^{'}} - 72 y = 0, y (1) = e^{- 8 x}

y = c_{1} e^{9 x} + c_{2} e^{- 8 x}

Solution steps

y^{''} (x) - y^{'} (x) - 72 y = 0

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{- 8 x}

y = c_{1} e^{9 x} + c_{2} e^{- 8 x}

(D^{3} - 4 D^{2} + 5 D) y = 0

y^{^{''}} + 10 y^{^{'}} - 24 y = 0

4 y^{^{''''}} - 5 y^{^{''}} - 9 y = 0

y^{^{'''}} - 3 y^{^{''}} - 34 y^{^{'}} - 48 y = 0

y^{^{''}} - \frac{3}{2} y^{^{'}} - y = 0

What is the solution for y^{''}-y^'-72y=0,y(1)=e^{-8x} ?
The solution for y^{''}-y^'-72y=0,y(1)=e^{-8x} is y=c_{1}e^{9x}+c_{2}e^{-8x}