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

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

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

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

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

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 5 e^{2 x}

Solve linear ODE:

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

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

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