Differential Equations Question 281
Question: What is the degree of the differential equation $ {{( \frac{d^{3}y}{dx^{3}} )}^{2/3}}+4-3( \frac{d^{2}y}{dx^{2}} )+5( \frac{dy}{dx} )=0 $ -
Options:
A) 3
B) 2
C) 2/3
D) Not defined
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Degree of a differential equation is the power to which the highest derivative is raised when it is expressed as polynomial of derivatives. Given equation is $ {{( \frac{d^{3}y}{dx^{3}} )}^{2/3}}-3( \frac{d^{2}y}{dx^{2}} )+5( \frac{dy}{dx} )+4=0 $
$ \Rightarrow {{( \frac{d^{3}y}{dx^{3}} )}^{2/3}}=3\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}-4 $ Cube on both side. $ {{( \frac{d^{3}y}{dx^{3}} )}^{2}}={{[ 3\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}-4 ]}^{3}} $ Hence, degree = 2
BETA
