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

The solution for y^{''}-2y^'+y=e^xsech^2(x) is y=c_{1}e^x+c_{2}xe^x+e^xln(cosh(x))

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

What is the solution for y^{''}-2y^'+y=e^xsech^2(x) ?
The solution for y^{''}-2y^'+y=e^xsech^2(x) is y=c_{1}e^x+c_{2}xe^x+e^xln(cosh(x))