Solve the initial value problem. √y dx + (2 + x)dy = 0, y(-1)=64 The solution is (Type an implicit solution. Type an equation using x and y as the variables.)
Solve the initial value problem. √y dx + (2 + x)dy = 0, y(-1)=64 The solution is (Type an implicit solution. Type an equation using x and y as the variables.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Problem Statement
**Objective:** Solve the initial value problem given below:
\[
\sqrt{y} \, dx + (2 + x) \, dy = 0, \quad y(-1) = 64
\]
**Instructions:** Provide the solution as an implicit equation involving the variables \(x\) and \(y\).
### Your Task
The solution must be entered in the designated box. Ensure that the equation you provide smoothly integrates both variables and addresses the initial condition appropriately.
**Note:** The response must be an implicit solution—an expression that involves both \(x\) and \(y\) together, instead of explicitly solving for one variable in terms of the other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F799db758-6264-477e-875f-1cfecc426da7%2F37c20397-a7a6-4147-ab96-7f625f1fea9d%2F1ur6g7dl_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Objective:** Solve the initial value problem given below:
\[
\sqrt{y} \, dx + (2 + x) \, dy = 0, \quad y(-1) = 64
\]
**Instructions:** Provide the solution as an implicit equation involving the variables \(x\) and \(y\).
### Your Task
The solution must be entered in the designated box. Ensure that the equation you provide smoothly integrates both variables and addresses the initial condition appropriately.
**Note:** The response must be an implicit solution—an expression that involves both \(x\) and \(y\) together, instead of explicitly solving for one variable in terms of the other.
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