What is the solution for y^{''}-2y^'+y=e^{2x}+x+1 ?

The solution for y^{''}-2y^'+y=e^{2x}+x+1 is y=c_{1}e^x+c_{2}xe^x+e^{2x}+x+3

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

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

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

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = e^{2 x} + x + 1

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} + 6 y = (20 x + 11) e^{x}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 7 + e^{\frac{x}{2}}

V^{^{''}} + 25 \cdot 1 0^{2} V^{^{'}} + 25 \cdot 1 0^{6} V = 5 \cdot 1 0^{8}

y^{^{''}} + 49 y = 6 cos (7 x) + 9 sin (7 x)

3 y^{^{''}} - 6 y^{^{'}} + 30 y = 15 sin (x)

What is the solution for y^{''}-2y^'+y=e^{2x}+x+1 ?
The solution for y^{''}-2y^'+y=e^{2x}+x+1 is y=c_{1}e^x+c_{2}xe^x+e^{2x}+x+3