What is the solution for x(x-1)y^{''}-xy^'+y=0 ?

The solution for x(x-1)y^{''}-xy^'+y=0 is y=e^{c_{1}}xln(x)+e^{c_{1}}+c_{2}x

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x(x-1)y^{''}-xy^'+y=0

x (x - 1) y^{^{''}} - x y^{^{'}} + y = 0

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

Solution steps

x (x - 1) y^{''} (x) - x y^{'} (x) + y = 0

Solve using substitution:

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

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

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What is the solution for x(x-1)y^{''}-xy^'+y=0 ?
The solution for x(x-1)y^{''}-xy^'+y=0 is y=e^{c_{1}}xln(x)+e^{c_{1}}+c_{2}x