Q.274. Differential equation.

Question 274.
Solve the Differential Equation.
x^2 { dy/dx + y/(x - 1) } + 2xy = 1/(x - 1)^2.

Answer 274.
x^2 [dy/dx + y/(x - 1)] + 2xy = 1/(x-1)^2
Multiplying the equation by (x - 1),
=> x^2 (x - 1) dy/dx + x^2 y + 2xy (x - 1) = 1/(x - 1)
=> d/dx [yx^2(x-1)] = 1/(x - 1)

Integrating,
yx^2 (x - 1) = ln lx - 1l + c
=> y = [ln lx - 1l] / [x^2(x - 1)] + c/[x^2(x - 1)].

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