Differential Equations Question 200
Question: The solution of the differential equation $ \frac{dy}{dx}=\frac{3x^{2}y^{4}+2xy}{x^{2}-2x^{3}y^{3}} $ is
Options:
A) $ \frac{y^{2}}{x}-x^{3}y^{2}=c $
B) $ \frac{x^{2}}{y^{2}}+x^{3}y^{3}=c $
C) $ \frac{x^{2}}{y}+x^{3}y^{2}=c $
D) $ \frac{x^{2}}{3y}-x^{3}y^{2}=c $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Rewrite the differential equation as $ (2xydx-x^{2}dy)+y^{2}(3x^{2}y^{2}dx+2x^{3}ydy)=0 $ Dividing by $ y^{2} $ ,
we get $ \frac{y2xdx-x^{2}dy}{y^{2}}+y^{2}3x^{2}dx+x^{3}2ydy=0 $ Or $ d( \frac{x^{2}}{y} )+d( x^{2}y^{2} )=0 $
Integrating, we get the solution $ \frac{x^{2}}{y}+x^{3}y^{2}=c $
BETA
