A homogeneous differential equation of the fo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$,the variables are expressed as a function of the r

Vedclass · Accepted Answer

$x = vy$

Vedclass · Answer

(A) For a homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$,the variables are expressed as a function of the ratio $\frac{x}{y}$.To solve this,we substitute $x = vy$,where $v$ is a function of $y$.By differentiating $x = vy$ with respect to $y$,we get $\frac{dx}{dy} = v + y\frac{dv}{dy}$.Substituting this into the original equation allows us to separate the variables $v$ and $y$.Therefore,the correct substitution is $x = vy$.Hence,the correct option is $A$.

$A$ homogeneous differential equation of the form $\frac{dx}{dy} = h\left(\frac{x}{y}\right)$ can be solved by making the substitution:

Similar Questions

The solution of the differential equation $y \sin \left(\frac{x}{y}\right) dx = \left\{x \sin \left(\frac{x}{y}\right) - y\right\} dy$ satisfying $y\left(\frac{\pi}{4}\right) = 1$ is

The solution of the differential equation $x + y\frac{dy}{dx} = 2y$ is

The solution of the differential equation $x dy - y dx = \sqrt{x^2+y^2} dx$, given that $y=1$ when $x=\sqrt{3}$, is

The general solution of the differential equation $\frac{d y}{d x}=\frac{x+7 y+3}{3 x+5 y+9}$ is

Which of the following is not a homogeneous function?

Vedclass Test Series

Exam Paper Generator

Online Exam Module