Differential Equations Question 212
Question: Solution of differential equation $ x\frac{dy}{dx}=y+{x^{^{2}}} $ is
[MP PET 1997]
Options:
A) $ y={\log _{e}}x+\frac{x^{2}}{2}+a $
B) $ y=\frac{x^{3}}{3}+\frac{a}{x} $
C) $ y=x^{2}+ax $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}-\frac{y}{x}=x $ ; I.F. $ ={e^{\int _{{}}^{{}}{-\frac{1}{x}dx}}}=\frac{1}{x} $
$ \therefore $ Solution is $ y\cdot \frac{1}{x}=\int _{{}}^{{}}{x\cdot \frac{1}{x}dx} $
Therefore $ \frac{y}{x}=x+a $
Therefore $ y=x^{2}+ax $ .
BETA
