Question

The solutions of $x^2{y}_1^2+yx{y}_1-6y^2=0$ are:

• A. $y=C{x}^2$
• B. $x^{2}y=C$
• C. $\frac{1}{2}\log y=C+\log x$
• D. $x^{3}y=C$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $y=C{x}^2$
C $\frac{1}{2}\log y=C+\log x$
D $x^{3}y=C$

Solving for $\frac{dy}{dx}$, we get $(x\frac{dy}{dx}+3y)(x\frac{dy}{dx}-2y)=0$
$\Rightarrow x\frac{dy}{dx}+3y=0\Rightarrow \frac{dy}{y}=-3\frac{dx}{x}\Rightarrow y{x}^3=C$
or $x\frac{dy}{dx}-2y=0\Rightarrow y=C{x}^2$ or $\frac{1}{2}\log y=C+\log x$