Question

A homogeneous differential equation of the from $\frac{dx}{dy}=h \biggr\lgroup \frac xy \biggr\rgroup$ can be solved by making the substitution.
(A) y = vx
(B) v = yx
(C) x = vy
(D) x = v

Answer 1

see the picture
and I hope u r satisfied

Answer 2

Answer:

(C)x = vy

Step-by-step explanation:

In this question,

Take x = vy

Differentiating with respect to y we get,

$\frac{dy}{dx}\ =\ v\ +\ \frac{dv}{dy}$

Now, Putting the values of $\frac{dy}{dx}\ in\ \mathbf{\frac{dx}{dy} = h[\frac{x}{y}}]$

$v\ +\ y\frac{dv}{dy}\ =\ h[v]$

As, $\frac{x}{y}\ =\ v$

$h[v]\ -\ v\ =\ y\frac{dv}{dy}$

$\mathbf{\int{\frac{dv}{h[v]\ -\ v}}\ =\ \frac{dy}{y}}$

Hence by making the substitution x = vy the given homogeneous differential equation can be solved.

Therefore option C is correct