dy dx =x√√√y; y(2) = 4

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Differential Equation Analysis**

Given: 

\[ \frac{dy}{dx} = x\sqrt{y} \]
\[ y(2) = 4 \]

This equation is labeled as "separable" in red ink, indicating that it can be solved by separation of variables.

**Explanation:**

The equation is a first-order differential equation, which appears to be separable. This means it can be rewritten in a form where all terms involving \( y \) are on one side, and all terms involving \( x \) are on the other, allowing for integration. The initial condition \( y(2) = 4 \) provides a specific solution to the equation.
Transcribed Image Text:**Differential Equation Analysis** Given: \[ \frac{dy}{dx} = x\sqrt{y} \] \[ y(2) = 4 \] This equation is labeled as "separable" in red ink, indicating that it can be solved by separation of variables. **Explanation:** The equation is a first-order differential equation, which appears to be separable. This means it can be rewritten in a form where all terms involving \( y \) are on one side, and all terms involving \( x \) are on the other, allowing for integration. The initial condition \( y(2) = 4 \) provides a specific solution to the equation.
Expert Solution
Step 1

Variable Separable Differential Equations

The differential equations which are expressed in terms of (x,y) such that, the x-terms and y-terms can be separated to different sides of the equation (including delta terms). Thus each variable separated can be integrated easily to form the solution of differential equation.

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