Question

The equation of curve passing through $(3,4)$ and satisfying the differential equation $y{\left(\frac{dy}{dx}\right)}^2+(x-y)\frac{dy}{dx}-x=0$ is

• A. $x-y+1=0$
• B. $x+y+1=0$
• C. $x+y-1=0$
• D. $2x+y-1=0$

Answer 1

Answer: (A)

$y{\left(\frac{dy}{dx}\right)}^2+x\frac{dy}{dx}-y\frac{dy}{dx}-x=0$
$y\frac{dy}{dx}\left(\frac{dy}{dx}-1\right)+x\left(\frac{dy}{dx}-1\right)=0$
$\left(y\frac{dy}{dx}+x\right)\left(\frac{dy}{dx}-1\right)=0$
$\therefore$ either $ydy+xdx=0$ or $dy-dx=0$
since the curves pass through the point $(3,4)$
$\therefore x^2+y^2=25$ or $x-y+1=0$