Question

The solution of $\frac{dy}{dx}=\left(\frac{ax+b}{cy+d}\right)$ represents a parabola if:-

• A. a=0,c=0
• B. a=1,c=2
• C. a=0,$c\ne 0$
• D. a=1,c=1

Answer 1

Answer: (C)

a=0,$c\ne 0$

We hyave,

$\frac{dy}{dx}=\frac{ax+b}{cy+d}$

For above differential equation to represent equation of parabola, one variable must have highest degree $2$ and other must have degree $1$.

When we take $a=0$ and $c\ne 0$, then we get

$\frac{dy}{dx}=\frac{0+b}{cy+d}$

$(cy+d)dy=bdx$

$\int (cy+d)dy=\int bdx$

$\frac{c{y}^2}{2}+dy=bx+C$ which is equation of parabola.

Hence, this is the answer.