Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
3.2k views
in Differential Equations by (28.7k points)
closed by

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

y = px + \(\sqrt{a^2p^2 + b^2}\), where p = \(\frac{dy}{dx}\)

1 Answer

+1 vote
by (29.1k points)
selected by
 
Best answer

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

First of all, we will rearrange the above equation as follows

here we have substituted the value of p and taken a2 out from the root

Since the above equation has rational powers we need to remove them so squaring on both sides.

So, the order of the above differential equation 1 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constants or independent variable, then the equation is linear.

So, in this question the dependent variable is y and the term \(\frac{dy}{dx}\) is multiplied by itself, so the given equation is non-linear.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...