Determine the order and degree (if defined) o | vedclass

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

Question

(C) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$. The order of a differential equ

Vedclass · Accepted Answer

Order $2$,Degree not defined

Vedclass · Answer

(C) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,so the order is $2$. The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in its derivatives. In this equation,the term $\cos \left(\frac{d y}{d x}\right)$ involves a transcendental function of the derivative,which means the equation cannot be expressed as a polynomial in terms of its derivatives. Therefore,the degree of this differential equation is not defined.

Determine the order and degree (if defined) of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$.

Similar Questions

The order of the differential equation,whose general solution is given by $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$,where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constants,is

The order and degree of the differential equation $y=px+\sqrt{a^{2}p^{2}+b^{2}}$,where $p=\frac{dy}{dx}$,are respectively:

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$ are respectively:

The order and degree of the differential equation $y = x \frac{dp}{dx} + \sqrt{a^{2} p^{2} + b^{2}}$,where $p = \frac{dy}{dx}$ (here $a$ and $b$ are arbitrary constants) respectively are:

The order of the differential equation whose general solution is given by $y = C_1 e^{2x + C_2} + C_3 e^x + C_4 \sin(x + C_5)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module