Differential Equations Question 206
Question: The solution of the differential equation $ y(2x^{4}+y)\frac{dy}{dx}=(1-4xy^{2})x^{2} $ is given by
Options:
A) $ 3{{(x^{2}y)}^{2}}+y^{3}-x^{3}=c $
B) $ xy^{2}+\frac{y^{3}}{3}-\frac{x^{3}}{3}+c=0 $
C) $ \frac{2}{3}yx^{5}+\frac{y^{3}}{3}=\frac{x^{3}}{3}-\frac{4xy^{3}}{3}+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ y(2x^{4}+y)\frac{dy}{dx}=(1-4xy^{2})x^{2} $ Or $ 2x^{4}ydy+y^{2}dy+4x^{3}y^{2}dx-x^{2}dx=0 $ Or $ 2x^{2}y(x^{2}dy+2xydx)+y^{2}dy-x^{2}dx=0 $ Or $ 2x^{2}yd(x^{2}y)+y^{2}dy-x^{2}dx=0 $ Integrating, we get $ {{(x^{2}y)}^{2}}+\frac{y^{3}}{3}-\frac{x^{3}}{3}=c $ Or $ 3{{(x^{2}y)}^{2}}+y^{3}-x^{3}=c $
BETA
