Mathematics

Problem

Consider the differential equation

\frac{dy}{dx} = \frac{y^3}{2(xy^2 - x^2)}

: Statement 1: The substitution

z = y^2

transforms the above equation into a first order homogeneous differential equation. Statement 2: The solution of this differential equation is

\ln(y^2) - \frac{y^2}{x} = C

. [JEE-MAIN ONLINE-2013] (1) Statement 1 is false and statement 2 is true. (2) Both statements are true. (3) Statement 1 is true and statement 2 is false. (4) Both statements are false.

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