Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 3xyy' = 3y2 + 8x/8x2 + y? %3D ....... For x, y >0, a general solution is (Type an implicit general solution in the form F(x,y)%3DC, where C is an arbitrary constant. Type an expression using x and y as th
Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 3xyy' = 3y2 + 8x/8x2 + y? %3D ....... For x, y >0, a general solution is (Type an implicit general solution in the form F(x,y)%3DC, where C is an arbitrary constant. Type an expression using x and y as th
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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![**Differential Equations: General Solution**
**Problem Statement:**
Find the general solution of the following differential equation. Primes denote derivatives with respect to \( x \).
\[ 3xyy' = 3y^2 + 8x\sqrt{8x^2 + y^2} \]
----------------------------------------------------------------------------
**Solution Instruction:**
For \( x, y > 0 \), a general solution is \(\Box\).
*Instructions:*
(Type an implicit general solution in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant. Type an expression using \( x \) and \( y \) as the variables.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215c9956-76b8-4988-9874-46d947288784%2F22d66019-518d-4d58-bacd-6c2fb53a9953%2F7wi8rup_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Differential Equations: General Solution**
**Problem Statement:**
Find the general solution of the following differential equation. Primes denote derivatives with respect to \( x \).
\[ 3xyy' = 3y^2 + 8x\sqrt{8x^2 + y^2} \]
----------------------------------------------------------------------------
**Solution Instruction:**
For \( x, y > 0 \), a general solution is \(\Box\).
*Instructions:*
(Type an implicit general solution in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant. Type an expression using \( x \) and \( y \) as the variables.)
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