Differential Equations Question 185
Question: Solution of $ \frac{dy}{dx}+2xy=y $ is
Options:
A) $ y=c{e^{x-x^{2}}} $
B) $ y=c{e^{x^{2}-x}} $
C) $ y=ce^{x} $
D) $ y=c{e^{-x^{2}}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{dy}{dx}+2xy=y $ Or $ \frac{dy}{dx}=y(1-2x) $ Or $ \frac{dy}{dx}=(1-2x)dx $ Or $ \log y=x-x^{2}+c_1 $ Or $ y={e^{x-x^{2}}}{e^{c_1}}=c{e^{x-x^{2}}} $ where $ c={e^{c_1}} $ Thus, $ y=c{e^{x-x^{2}}} $ is the required solution.
BETA
