Homogeneous De
To solve a homogeneous DE, we use the substitution
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About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- homogeneous de
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
y = vx
- Substitution Choice: For dxdy=F(xy), we let y=vx.
- Differentiatiation: Using the product rule:
- dxdy=v⋅(1)+x⋅dxdv=v+xdxdv.
- Application: Substitute both y and dxdy into the original equation:
- v+xdxdv=F(v)
- xdxdv=F(v)−v
- Separation: F(v)−vdv=xdx, which is now variable separable.
This easy difficulty mathematics question is from the chapter differential equations, covering the topic of homogeneous de. It appeared in the 2025 exam.
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