Differential Equations Question 294
Question: What is the solution of the differential equation $ \frac{dy}{dx}=\frac{y}{(x+2y^{3})} $ -
Options:
A) $ y(1-xy)=cx $
B) $ y^{3}-x=cy $
C) $ x(1-xy)=cy $
D) $ x(1+xy)=cy $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ y^{3}-x=cy $
$ \Rightarrow 3y^{2}\frac{dy}{dx}-1=c\frac{dy}{dx}\Rightarrow \frac{dy}{dx}(3y^{2}-c)=1 $
$ \Rightarrow \frac{dy}{dx}( 3y^{2}-\frac{y^{3}-x}{y} )=1 $
$ \Rightarrow \frac{dy}{dx}( \frac{3y^{3}-y^{3}+x}{y} )=1\Rightarrow \frac{dy}{dx}=\frac{y}{x+2y^{3}} $
BETA
