Search any question & find its solution
Question:
Answered & Verified by Expert
If $x \frac{d y}{d x}+y=\frac{x f(x y)}{f^{\prime}(x y)}$, then $|f(x y)|$ is equal to
Options:
Solution:
2465 Upvotes
Verified Answer
The correct answer is:
$k e^{x^{2} / 2}$
$x \frac{d y}{d x}+y=\frac{x f(x y)}{f^{\prime}(x y)} \Rightarrow \frac{x d y+y d x}{d x}=\frac{x f(x y)}{f^{\prime}(x y)} \Rightarrow \frac{f^{\prime}(x y) d(x y)}{f(x y)}=x d x \Rightarrow \ln f(x y)=\frac{x^{2}}{2}+C \Rightarrow|f(x y)|=k e^{x^{2} / 2}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.