Solve: dy/dx = y^2, y(0)=1.

Solve: dy/dx = y^2, y(0)=1.

Approach: Separate variables and integrate.

dy/y^2 = dx. Integrate: -1/y = x + C. Using y(0)=1: -1 = C. So -1/y = x - 1, y = 1/(1-x).

Follow-up: What is interval of existence?

Key concepts: separable ODE, integration, initial condition.