(y² + xy)dx-x²dy = 0
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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![On this page, we discuss a first-order differential equation. The given differential equation is:
\[
(y^2 + xy) dx - x^2 dy = 0
\]
Explanation:
- \( (y^2 + xy) dx \) and \( -x^2 dy \) are terms involving both \(x\) and \(y\).
- \( dx \) and \( dy \) signify the differentials of \(x\) and \(y\), respectively.
- This equation is set to zero, indicating it is a homogeneous differential equation.
To solve differential equations like this, you would typically separate the variables and integrate each side accordingly. This type of equation is useful in various applications, including physics and engineering.
If you require further assistance in solving or understanding this differential equation, feel free to explore our advanced topics or contact our support team!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6aad8a00-c703-485c-bf76-99694ae31b4b%2Ff07b1237-62ef-42f7-8ba2-d55a581b30a3%2Fbdhsubk_processed.png&w=3840&q=75)
Transcribed Image Text:On this page, we discuss a first-order differential equation. The given differential equation is:
\[
(y^2 + xy) dx - x^2 dy = 0
\]
Explanation:
- \( (y^2 + xy) dx \) and \( -x^2 dy \) are terms involving both \(x\) and \(y\).
- \( dx \) and \( dy \) signify the differentials of \(x\) and \(y\), respectively.
- This equation is set to zero, indicating it is a homogeneous differential equation.
To solve differential equations like this, you would typically separate the variables and integrate each side accordingly. This type of equation is useful in various applications, including physics and engineering.
If you require further assistance in solving or understanding this differential equation, feel free to explore our advanced topics or contact our support team!
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