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

The solution for x^2y^{''}-xy^'+y=2x is y=c_{1}x+c_{2}ln(x)x+xln^2(x)

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x^2y^{''}-xy^'+y=2x

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (x + x + 3)

\int_{3}^{7} x x - 3 d x

\frac{1}{2} ln (\frac{1 + x}{1 - x})

\int 1. 8^{0.045 x} - 1 d x

\frac{d}{d x} (e^{c o s^{2} (x)})

What is the solution for x^2y^{''}-xy^'+y=2x ?
The solution for x^2y^{''}-xy^'+y=2x is y=c_{1}x+c_{2}ln(x)x+xln^2(x)