Differential Equations Question 98
Question: $ y=\frac{x}{x+1} $ is a solution of the differential equation
Options:
A) $ y^{2}\frac{dy}{dx}=x^{2} $
B) $ x^{2}\frac{dy}{dx}=y^{2} $
C) $ y\frac{dy}{dx}=x $
D) $ x\frac{dy}{dx}=y $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=\frac{x}{x+1}\Rightarrow \frac{1}{y}=1+\frac{1}{x} $
$ -\frac{1}{y^{2}}\frac{dy}{dx}=0-\frac{1}{x^{2}} $
Therefore $ x^{2}\frac{dy}{dx}=y^{2} $ .
BETA
