Question

The solution of $\frac{dy}{dx}=\frac{ax+h}{by+k}$ represent a parabola if:

• A. $a=2,b=0$
• B. $a=2,b=2$
• C. $a=0,b=2$
• D. $a=0,b=0$

Answer 1

Answer: (A), (C)

The correct options are
A $a=2,b=0$
C $a=0,b=2$

$y^{\prime }=\frac{ax+h}{by+k}\Rightarrow \frac{dy}{dx}(k+by)=h+ax\Rightarrow \int \frac{dy}{dx}(k+by)dx=\int (h+ax)dx\Rightarrow \frac{b{y}^2}{2}+ky=\frac{a{x}^2}{2}+hx+c$
Represent parabola only when $a=0,b=2$ or $a=2,b=0$