Differential Equations Question 181
Question: The solution of the differential equation $ \frac{dy}{dx}+\frac{y}{x}=x^{2} $ is
Options:
A) $ 4xy=x^{4}+c $
B) $ xy=x^{4}+c $
C) $ \frac{1}{4}xy=x^{4}+c $
D) $ xy=4x^{4}+c $
Show Answer
Answer:
Correct Answer: A
Solution:
The given equation $ \frac{dy}{dx}+\frac{y}{x}=x^{2} $ is of the form $ \frac{dy}{dx}+Py=Q $ . So, I.F.= $ {e^{\int _{{}}^{{}}{\frac{1}{x}dx}}}={e^{\log x}}=x $
Hence required solution $ xy=\int _{{}}^{{}}{x.x^{2}dx+c} $
Therefore $ xy=\frac{x^{4}}{4}+c $
Therefore $ 4xy=x^{4}+c $ .
BETA
