Question

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: $y=Ax : xy'= y (x (\neq) 0)$

Answer 1

y = Ax
Differentiating both sides with respect to x, we get:

$y'=\frac{d}{dx}(Ax)$

$\Rightarrow y'=A$
Substituting the value of y' in the given differential equation, we get:
L.H.S.=$xy'=x.A=A.x=y$=R.H.S.

Hence, the given function is the solution of the corresponding differential equation.