Differential Equations Question 231
Question: The degree of the differential equation $ y(x)=1+\frac{dy}{dx}+\frac{1}{1.2}{{( \frac{dy}{dx} )}^{2}}+\frac{1}{1.2.3}{{( \frac{dy}{dx} )}^{3}}+… $ is
[Orissa JEE 2005]
Options:
A) 2
B) 3
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=1+t+\frac{t^{2}}{2!}+\frac{t^{3}}{3!}+…+\infty $ where $ t=\frac{dy}{dx} $
Therefore $ y=e^{t} $ , \ $ t=\log y $
Therefore $ \frac{dy}{dx}=\log y $ . Hence degree is 1.
BETA
