Differential Equations Question 182
Question: If $ y=\frac{x}{\log | cx |} $ (where c is an arbitrary constant) I the general solution of the differential equation $ dy/dx=y/x+\phi (x/y) $ then the function $ \phi (x/y) $ is
Options:
A) $ x^{2}/y^{2} $
B) $ -x^{2}/y^{2} $
C) $ y^{2}/x^{2} $
D) $ -y^{2}/x^{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ \log c+\log | x |=\frac{x}{y} $ Differentiating w.r.t. x, $ \frac{1}{x}=\frac{y-x\frac{dy}{dx}}{y^{2}} $ Or $ \frac{y^{2}}{x}=y-x\frac{dy}{dx} $ Or $ \frac{dy}{dx}=\frac{y}{x}-\frac{y^{2}}{x^{2}} $ Or $ \phi ( \frac{x}{y} )=-\frac{y^{2}}{x^{2}} $
BETA
