7.7 Particular Solutions

Using an initial condition

An initial condition is a point (x, y) the solution passes through. Substitute it into the general solution to solve for C.

Result

Once C is determined, the general solution becomes the particular solution that satisfies the initial condition.

Key terms

Particular solution

The one satisfying a given initial condition.

Initial condition

A point (x, y) on the solution.

Find C

Substitute the point into the general solution.

General → particular

Determining C makes it particular.

Use

Pins down a single curve from the family.

Try an AP-style question

Solve dy/dx = 2x with y(0) = 3.

1. y = x² + 3
2. y = 2x + 3
3. y = x² − 3
4. y = x² + 3x