Which of the following equations is non-linea | vedclass

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

Question

(D) differential equation is linear if the dependent variable $y$ and its derivatives appear only in the first degree and are not multiplied together.

Vedclass · Accepted Answer

$x\frac{dy}{dx} + \frac{3}{dy/dx} = y^2$

Vedclass · Answer

(D) differential equation is linear if the dependent variable $y$ and its derivatives appear only in the first degree and are not multiplied together.For option $(d)$,we have $x\frac{dy}{dx} + \frac{3}{dy/dx} = y^2$.Multiplying both sides by $\frac{dy}{dx}$,we get $x\left(\frac{dy}{dx}\right)^2 - y^2\frac{dy}{dx} + 3 = 0$.Since the degree of the derivative $\frac{dy}{dx}$ is $2$,this differential equation is non-linear.

Which of the following equations is non-linear?

Similar Questions

The order and degree of the differential equation $3 x^2 \frac{d^2 y}{d x^2}-\sin \left(\frac{d^3 y}{d x^3}\right)+\cos (x y)=0$ are

The order and degree of the differential equation $\frac{d^2y}{dx^2} = \left\{ y + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}$ are:

If the order and degree of the differential equation $\left(\frac{d^2 y}{dx^2}\right)^5 + 4 \frac{\left(\frac{d^2 y}{dx^2}\right)^5}{\left(\frac{d^3 y}{dx^3}\right)} + \frac{d^3 y}{dx^3} = \sin x$ are $m$ and $n$ respectively,then the value of $(m^2 + n^2)$ is equal to

The order and degree of the differential equation $\frac{d^2y}{dx^2} = \cos \left( \frac{dy}{dx} \right) + xy$ are respectively-

Order of the differential equation of the family of all concentric circles centered at $(h, k)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module