How to solve
A separable ODE factors so all y dependence can sit with dy and all x dependence with dx. Rewriting dy/dx = g(x)h(y) as dy/h(y) = g(x) dx prepares both sides for independent integration.
Steps
- Start from dy/dx = g(x)h(y).
- Move y-factors with dy and x-factors with dx: dy/h(y) = g(x) dx.
- Write that separated form as the answer when the drill asks for setup only.
Example
Separate variables for dy/dx = xy.
- Write dy/dx = x · y.
- Divide by y (assuming y ≠ 0): dy/y = x dx.
Answer: dy/y = x dx
How to type answers
- Enter like dy/y = x dx
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