The solution of the differential equation x^2(y+1) \frac{d y}{d x}+y^2(x+1)^2=0, when y(1)=2, is [AP EAPCET 24 May 2025 S1]

Correct Answer is : log|12x2y|=1x+1y−x−12

\log {| x^2 y |}=\frac{2}{x}+\frac{1}{y}+x-1

\log {| \frac{1}{4} x^2 y |}=\frac{1}{x}+\frac{2}{y}+x-1

\log {| \frac{1}{2} x^2 y |}=\frac{1}{x}+\frac{1}{y}-x-\frac{1}{2}

\log {| \frac{1}{3} x^2 y |}=\frac{1}{x}+\frac{1}{y}-x+\frac{1}{2}

Differential Equations

Section: Mathematics

Question : 7 of 48

Marks: +1, -0

The solution of the differential equation x2(y+1)‌

+y2(x+1)2=0, when y(1)=2, is

[AP EAPCET 24 May 2025 S1]

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