Differential Equations › Section B · First order differential equations › Topic B.5
Substitutions
Many equations that fit none of the standard types become separable after the right change of variable. Two patterns, ratios y/x and combinations ax + by, cover a large share of the equations you will meet, and spotting them is a skill of pattern recognition.
In this topic
- Change the variable, change the equation
- Homogeneous equations
- The substitution y = xv
- Worked example: a homogeneous IVP
- Worked example: an implicit family
- Equations in ax + by + c
- Worked example: a combination x + y
- Choosing a substitution
- Common mistakes to avoid
- Key takeaways
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