Solve the equation. 3 2 dx ² = 6x² (9+ y²) An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. (Type an expression using x and y as the variables.)
Solve the equation. 3 2 dx ² = 6x² (9+ y²) An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. (Type an expression 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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Question
![**Solving Differential Equations**
In this exercise, you are asked to solve the given differential equation and find an implicit solution in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant.
**Given Differential Equation:**
\[
\frac{dy}{dx} = 6x^2 \left(9 + y^2\right)^{\frac{3}{2}}
\]
### Steps to Solve the Equation:
1. **Separate Variables:**
- To solve the differential equation, separate the variables \( x \) and \( y \).
2. **Integrate Both Sides:**
- Integrate the equation with respect to \( x \) and \( y \).
### Solution Format:
- The implicit solution should be expressed in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant.
**Fill-in the Solution:**
\[
F(x,y) = \boxed{\phantom{answer}} = C
\]
Remember to type the expression using \( x \) and \( y \) as the variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13d2fa52-7679-4dbf-8ccf-e0669bc97f10%2F053f2014-2f9b-4428-a57d-68b19fc53929%2Fm0feja_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving Differential Equations**
In this exercise, you are asked to solve the given differential equation and find an implicit solution in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant.
**Given Differential Equation:**
\[
\frac{dy}{dx} = 6x^2 \left(9 + y^2\right)^{\frac{3}{2}}
\]
### Steps to Solve the Equation:
1. **Separate Variables:**
- To solve the differential equation, separate the variables \( x \) and \( y \).
2. **Integrate Both Sides:**
- Integrate the equation with respect to \( x \) and \( y \).
### Solution Format:
- The implicit solution should be expressed in the form \( F(x,y) = C \), where \( C \) is an arbitrary constant.
**Fill-in the Solution:**
\[
F(x,y) = \boxed{\phantom{answer}} = C
\]
Remember to type the expression using \( x \) and \( y \) as the variables.
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