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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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