If frac{dy}{dx} = f(x, y) is a homogeneous di | vedclass

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

Question

(C) differential equation of the form $\frac{dy}{dx} = f(x, y)$ is said to be a homogeneous differential equation if the function $f(x, y)$ is a homog

Vedclass · Accepted Answer

$\phi\left(\frac{y}{x}\right)$

Vedclass · Answer

(C) differential equation of the form $\frac{dy}{dx} = f(x, y)$ is said to be a homogeneous differential equation if the function $f(x, y)$ is a homogeneous function of degree zero. By definition,a function $f(x, y)$ is homogeneous of degree zero if $f(\lambda x, \lambda y) = \lambda^0 f(x, y) = f(x, y)$. Such a function can always be expressed in the form $f(x, y) = \phi\left(\frac{y}{x}\right)$ or $f(x, y) = \psi\left(\frac{x}{y}\right)$. Therefore,the general form of $f(x, y)$ for a homogeneous differential equation $\frac{dy}{dx} = f(x, y)$ is $\phi\left(\frac{y}{x}\right)$.

If $\frac{dy}{dx} = f(x, y)$ is a homogeneous differential equation,then the general form of $f(x, y)$ is

Similar Questions

The particular solution of the differential equation,$x y \frac{dy}{dx} = x^2 + 2y^2$ when $y(1) = 0$ is

Three fair coins are tossed. If both heads and tails appear,then the probability that exactly one head appears is:

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

The solution of $x dy - y dx = \sqrt{x^2 + y^2} dx$ when $y(\sqrt{3}) = 1$ is

The slope of the tangent at $(x, y)$ to a curve passing through a point $(2, 1)$ is $\frac{x^2 + y^2}{2xy}$,then the equation of the curve is

Vedclass Test Series

Exam Paper Generator

Online Exam Module