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
223 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.

\(\frac{d^2y}{dx^2}+3 \left(\frac{dy}{dx} \right)^2\) \(= x^2\, \text{log} \left(\frac{d^2y}{dx^2}\right)\)

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.

Concept of the question

For the degree to be defined of any differential equation the euqtion must be expressible in the form of a polynomial.

But, in this question the degree of the differential equation is not defined because the term on the right hand side is not expressible in the form of a polynomial.

Thus, the order of the above equation is 2 whereas the degree is not defined.

Since the degree of the equation is not defined the 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

...