What is the solution for y^{''}-10y^'-171y=0,y(0)=9,y^'(0)=3 ?

The solution for y^{''}-10y^'-171y=0,y(0)=9,y^'(0)=3 is y=3e^{19t}+6e^{-9t}

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y^{''}-10y^'-171y=0,y(0)=9,y^'(0)=3

y^{^{''}} - 10 y^{^{'}} - 171 y = 0, y (0) = 9, y^{^{'}} (0) = 3

y = 3 e^{19 t} + 6 e^{- 9 t}

Solution steps

y^{''} (t) - 10 y^{'} (t) - 171 y = 0

Solve linear ODE:

y = 3 e^{19 t} + 6 e^{- 9 t}

y = 3 e^{19 t} + 6 e^{- 9 t}

y^{^{''}} - 19 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 9 y = 0, y (\frac{π}{2}) = 6, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 4

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 22

y^{^{''}} + \frac{1}{r} y^{^{'}} = 0

What is the solution for y^{''}-10y^'-171y=0,y(0)=9,y^'(0)=3 ?
The solution for y^{''}-10y^'-171y=0,y(0)=9,y^'(0)=3 is y=3e^{19t}+6e^{-9t}