How to solve
A differential equation assigns a slope to every point: plug (x, y) into f to read the slope there.
Steps
- Identify f(x, y) from y' = f(x, y).
- Substitute the given x and y.
- Simplify — that number is the slope of the solution through that point.
Example
y' = x² − 2y at (3, 1). Slope?
- 3² − 2·1 = 9 − 2.
- Slope = 7.
Answer: 7
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