Question

The solution of the differential equation, $\frac{dy}{dx}=\frac{y-x}{y-x-1}$, given $y(-5)=-5$ represents

• A. a pair of straight lines
• B. a circle
• C. parabola
• D. hyperbola

Answer 1

Answer: (C)

Answer is $(y-x{)}^2-2y=10$
Put $y-x=t\Rightarrow \frac{dy}{dx}=\frac{dt}{dx}+1$;
hence $\frac{dt}{dx}+1=\frac{t}{t-1}\Rightarrow \frac{dt}{dx}=\frac{t}{t-1}-1=\frac{t-t+1}{t-1}$
$\frac{dt}{dx}=\frac{1}{t-1};\frac{(t-1{)}^2}{2}=x+C$
$(y-x-1{)}^2=2x+C;C=9$