Homogeneous ode (class A)

3.3.7 Homogeneous ode (class A)

3.3.7.1 Example 1
3.3.7.2 Example 2
3.3.7.3 Example 3
3.3.7.4 Example 4
3.3.7.5 Example 5
3.3.7.6 Example 6
3.3.7.7 Example 7
3.3.7.8 Example 8
3.3.7.9 Example 9

y^{'} = F (\frac{y}{x})

ode internal name "homogA"

This is called Homogeneous type A in Maple. Solved by substituting $y = u x$ which converts it to separable ode. A homogeneous ode has the form $y^{'} = f (x, y)$ where $t f (x, y) = f (t x, t y)$ . In solving these types of problems, separable is called. It is best to return implicit solution from separable and not explicit. This makes the substitution $u = \frac{y}{x}$ easier. If explicit solution is needed, it can be done after this operation is done.

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