The general solution of the differential equation $(1+x^2)dy-xdx=0$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{e^{2y}}{1+x^2}=C$
$(1+x^2)dy-xdx=0$
$⇒\int dy=\int \frac{x}{1+x^2}dx$
$=\int dy = \frac{1}{2}\int\frac{2x}{1+x^2}dx$
$=y=\frac{1}{2}\log(1+x^2)+\log C$
$=2y=\log(1+x^2)+\log C$
$C(1+x^2)=e^{2y}⇒C=\frac{e^{2y}}{1+x^2}$