Question

For the differential equation $x \frac{dy}{dx}+2y=xy \frac{dy}{dx}$,

• A. order is $1$ and degree is $1$
• B. solution is $ln(yx^2) = C - y$
• C. order is $1$ and degree is $2$
• D. solution is $ln(xy^2) = C + y$

Answer 1

Answer: (A)

Given, $x \frac{dy}{dx}\left(1-y\right)+2y=0$
$\Rightarrow \left(\frac{1-y}{y}\right)dy+2 \frac{dx}{x}=0$
$\Rightarrow ln\,y-y+2\,ln\,x=C$
$\Rightarrow ln\left(yx^{2}\right)=C+y$