Question

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

• A. $x-y+1=0$
• B. $x^2+y^2=25$
• C. $\frac{x^2}{9}+\frac{y^2}{16}=2$
• D. $x+y-7=0$

Answer 1

Answer: (A), (B)

The correct options are
A $x-y+1=0$
B $x^2+y^2=25$

Given equation in $\frac{dy}{dx}$ can be factorised as
$(y\frac{dy}{dx}+x)(\frac{dy}{dx}-1)=0$
$\frac{dy}{dx}=-\frac{x}{y}$ or $\frac{dy}{dx}=1$
$xdx+ydy=0$ or $dy=dx$
Integrating both equations,
$x^2+y^2=c_1$ or $y=x+c_2$
$C_1=25,C_2=1$
$\Rightarrow x^2+y^2=25orx-y+1=0$