What is the solution for y^{''}-y^'-6y=0,y(ln^2(x))=5,y(0)=1 ?

The solution for y^{''}-y^'-6y=0,y(ln^2(x))=5,y(0)=1 is y=c_{1}e^{3x}+c_{2}e^{-2x}

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y^{''}-y^'-6y=0,y(ln^2(x))=5,y(0)=1

y^{^{''}} - y^{^{'}} - 6 y = 0, y (ln^{2} (x)) = 5, y (0) = 1

y = c_{1} e^{3 x} + c_{2} e^{- 2 x}

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 0

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x}

What is the solution for y^{''}-y^'-6y=0,y(ln^2(x))=5,y(0)=1 ?
The solution for y^{''}-y^'-6y=0,y(ln^2(x))=5,y(0)=1 is y=c_{1}e^{3x}+c_{2}e^{-2x}