Differential Equations Question 196
Question: The solution of differential equation $ (2y+xy^{3})dx+(x+x^{2}y^{2})dy=0 $ is
Options:
A) $ x^{2}y+\frac{x^{3}y^{3}}{3}=c $
B) $ xy^{2}+\frac{x^{3}y^{3}}{3}=c $
C) $ x^{2}y+\frac{x^{4}y^{4}}{4}=c $
D) none of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ (2x+xy^{3})dx+(x+x^{2}y^{2})dy=0 $
Or $ (2ydx+xdy)+(xy^{3}dx+x^{2}y^{2}dy)=0 $
Multiplying by x, we get $ (2xydx+x^{2}dy)+(x^{2}y^{3}dx+x^{3}y^{2}dy)=0 $ Or $ d(x^{2}y)+\frac{1}{3}d(x^{3}y^{3})=0 $
Integrating, we get $ x^{2}y+\frac{x^{3}y^{3}}{3}=c $
BETA
