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Separable Differential Equations
AP Calculus AB · Unit 7 Diff. Equations
Learning Objectives
Separate variables: g(y)dy = f(x)dx
Integrate both sides independently
Apply initial conditions to find C
Visualize solution curves with slope fields
Method
1. Write dy/dx = f(x)·g(y)
2. Separate: dy/g(y) = f(x)dx
3. Integrate: ∫dy/g(y) = ∫f(x)dx
4. Solve for y, apply IC
Tags
separable ODE
slope field
initial condition
EQUATION
dy/dx = xy (exponential growth)
dy/dx = −y/x
dy/dx = y(1−y) (logistic)
dy/dx = x/y
y₀ (initial)
1.0