Search any question & find its solution
Question:
Answered & Verified by Expert
If $x^\alpha \frac{d y}{d x}=y^\beta(\gamma \log x+\delta \log y+1)$ is a homogeneous differential equation, then
Options:
Solution:
1343 Upvotes
Verified Answer
The correct answer is:
$\alpha=\beta$ and $\gamma=-\delta$
Given, $x^\alpha \frac{d y}{d x}=y^\beta(\gamma \log x+\delta \log y+1)$
$\Rightarrow \frac{d y}{d x}=\frac{y^\beta}{x^\alpha}\left(\log x^\gamma \cdot y^\delta e\right)$
for homogeneous differential equation $\alpha=\beta$ and $\gamma=-\delta$.
$\Rightarrow \frac{d y}{d x}=\frac{y^\beta}{x^\alpha}\left(\log x^\gamma \cdot y^\delta e\right)$
for homogeneous differential equation $\alpha=\beta$ and $\gamma=-\delta$.
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.