05 Reduction of Order
General Form of 2nd order DEΒΆ
This is for variable coefficients.
SolvingΒΆ
- 2nd order DE is reduced into two 1st order DE
- they are solved one after each other
Reduction of order method is possible under 2 cases
Case 1 | Case 2 | |
---|---|---|
missing terms | Dependent variable | Independent variable |
Form | ||
Let | $y' = P \ | |
\implies y'' = P' = \frac{dP}{dy} y' \ y''= P \left(\frac{dP}{dy}\right)$ | ||
Solve | ||
Substitute | ||
Solve |