Question

Form an differential equation by eliminating the arbitrary constants from the equation:

$y=Ax+A^2$.

Answer 1

Given the equation:

$y=Ax+A^2$......(1)

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=A$

Now putting this value of $A$ in equation (1) we get,

$y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^2$.