Differential Equations Question 194
Question: The solution of the differential equation $ x\frac{dy}{dx}+y=x^{2}+3x+2 $ is
Options:
A) $ xy=\frac{x^{3}}{3}+\frac{3}{2}x^{2}+2x+c $
B) $ xy=\frac{x^{4}}{4}+x^{3}+x^{2}+c $
C) $ xy=\frac{x^{4}}{4}+\frac{x^{3}}{3}+x^{2}+c $
D) $ xy=\frac{x^{4}}{4}+x^{3}+x^{2}+cx $
Show Answer
Answer:
Correct Answer: A
Solution:
$ x\frac{dy}{dx}+y=x^{2}+3x+2 $
Therefore $ \frac{dy}{dx}+\frac{y}{x}=x+3+\frac{2}{x} $
Here $ P=\frac{1}{x},\ Q=x+3+\frac{2}{x} $ , therefore I.F. $ \frac{dy}{dx}=-1 $
Now solve it.
BETA
