Consider the differential equation

Question:

Consider the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}^{3}}{2\left(\mathrm{xy}^{2}-\mathrm{x}^{2}\right)}$ :

Statement 1 : The substitution $\mathrm{z}=\mathrm{y}^{2}$ transforms the above equation into a first order homogenous differential equation.

Statement 2 : The solution of this differential equation is $y^{2} e^{-\frac{y^{2}}{x}}=C$.

  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.


Correct Option: , 2

Solution:

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