Question

The solution of equation $\frac{dy}{dx}=\frac{ax+b}{cy+d}$ represents :

• A. A straight line if $a=c=0$ and $b,d\ne 0$
• B. A parabola if $a=2,c=0,d\ne 0$
• C. A huberbola if $b=d=0,a$ and $c\ne 0$
• D. A rectangular hyberbola of $b=d=0,a=c=2$

Answer 1

The correct option is A A straight line if $a=c=0$ and $b,d\ne 0$

Given Differential equation is $\frac{dy}{dx}=\frac{ax+b}{cy+d}$,

Separating the variables and integrating gives,

$\int (cy+d)dy=\int (ax+b)dx$,

$⟹\frac{c{y}^2}{2}+dy=\frac{a{x}^2}{2}+bx+K$,

Where $K$ is the integration constant,

If $a=c=0$ and $b,d\ne 0$, the equation becomes,

$dy-bx=K$ which representss a straight line.