Question

Solution of $y-x\frac{dy}{dx}=3[1-x^2\frac{dy}{dx}]$ is:

• A. $(y+3)(1+3x)=cx$
• B. $(y-3)(1-3x)=cx$
• C. $(y-3)(1+3x)=cx$
• D. $(y+3)(1-3x)=cx$

Answer 1

The correct option is B $(y-3)(1-3x)=cx$

$y-x\frac{dy}{dx}=3-3x^2\frac{dy}{dx}$

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

$\Rightarrow \frac{dx}{x-3x}=\frac{dy}{y-3}$

$\frac{dx}{(1-3x)}=\frac{dy}{y-3}$

$\Rightarrow \int \frac{3}{x-3x}+\frac{1}{x}dx=\int \frac{dy}{y-3}-logc$

$\Rightarrow -\log (1-3x)+\log x=\log (y-3)-\log c$

$\Rightarrow \log xc=\log (y-3)(1-3x)$

$\Rightarrow xc=(y-3)(1-3x)$