What is the solution for y^{''}-y^'-2y=4,x^2y(0)=1,y^'(0)=4 ?

The solution for y^{''}-y^'-2y=4,x^2y(0)=1,y^'(0)=4 is y=c_{1}e^{2x}+c_{2}e^{-x}-2

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

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

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

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 4

Solve linear ODE:

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

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

What is the solution for y^{''}-y^'-2y=4,x^2y(0)=1,y^'(0)=4 ?
The solution for y^{''}-y^'-2y=4,x^2y(0)=1,y^'(0)=4 is y=c_{1}e^{2x}+c_{2}e^{-x}-2