To solve the equation:

\[
\sqrt{2xy} \frac{dy}{dx} = 1
\]

We want to isolate \(\frac{dy}{dx}\). Let's break it down step by step.

### Step 1: Isolate \(\frac{dy}{dx}\)

Divide both sides of the equation by \(\sqrt{2xy}\):

\[
\frac{dy}{dx} = \frac{1}{\sqrt{2xy}}
\]

Now the equation is simpler:

\[
\frac{dy}{dx} = \frac{1}{\sqrt{2xy}}
\]

This is a separable differential equation, and you can solve it by separating the variables and then integrating.

Would you like the detailed solution for solving this equation, or do you have any specific questions?

---

Here are 5 related questions to consider:
1. How do we solve separable differential equations?
2. What are some techniques to handle square root terms in differential equations?
3. How do we handle initial conditions in this type of problem?
4. Can this equation be solved for a general solution in terms of \(x\) and \(y\)?
5. What types of functions involve square roots like \(\sqrt{xy}\)?

**Tip:** Always check if the differential equation can be separated easily into functions of \(x\) and \(y\), as this simplifies solving it.

Explore a detailed solution to the differential equation \sqrt{2xy}\frac{dy}{dx} = 1. Learn to solve separable differential equations and understand key techniques for handling square root expressions in calculus. Suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation