Use the method for solving homogeneous equations to solve the following differential equation. (9x² - y²) dx + (xy-4x³y-¹) dy=0 Ignoring lost solutions, if any, an implicit solution in the form F(x,y) = C is (Type an expression using x and y as the variables.) = C, where C is an arbitrary constant.
Use the method for solving homogeneous equations to solve the following differential equation. (9x² - y²) dx + (xy-4x³y-¹) dy=0 Ignoring lost solutions, if any, an implicit solution in the form F(x,y) = C is (Type an expression using x and y as the variables.) = C, where C is an arbitrary constant.
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 Homogeneous Differential Equations**
To solve the given homogeneous differential equation:
\[
(gx^2 - y^2) \, dx + \left(xy - 4x^3 y^{-1}\right) \, dy = 0
\]
**Solution Steps:**
1. **Identify and Simplify:**
Using the method for solving homogeneous equations, we start by simplifying the given equation.
2. **Formulate the Implicit Solution:**
Ignoring lost solutions, if any, an implicit solution in the form \( F(x, y) = C \) (where \( C \) is an arbitrary constant) can be derived.
**Exercise:**
Make sure to type an expression using \(x\) and \(y\) as the variables in the form box, as provided in the problem statement.
\[
\text{Implicit Solution in the form: } F(x, y) = C \text{, where C is a constant.}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe57d9078-3a26-4ab9-a5c6-f67f173c178d%2F45da509d-82b1-4cb0-9d37-599d23646aa9%2Fb6qv2qk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Homogeneous Differential Equations**
To solve the given homogeneous differential equation:
\[
(gx^2 - y^2) \, dx + \left(xy - 4x^3 y^{-1}\right) \, dy = 0
\]
**Solution Steps:**
1. **Identify and Simplify:**
Using the method for solving homogeneous equations, we start by simplifying the given equation.
2. **Formulate the Implicit Solution:**
Ignoring lost solutions, if any, an implicit solution in the form \( F(x, y) = C \) (where \( C \) is an arbitrary constant) can be derived.
**Exercise:**
Make sure to type an expression using \(x\) and \(y\) as the variables in the form box, as provided in the problem statement.
\[
\text{Implicit Solution in the form: } F(x, y) = C \text{, where C is a constant.}
\]
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