Download Particular Solutions to Differential Equations

Particular Solutions to
Differential Equations
Unit 4 Day 2
Do Now
 Write as many facts as you can relating f(x), f '(x), F(x),
F''(x), and the integral symbol.
Ex. 1
 What are some solutions of F ' = 3x – 2?
 What could we do to narrow this down to one solution?
Ex. 1A
 Find the particular solution of F ' = 3x – 2 that satisfies
the initial condition F(2) = 1.
Ex. 2
 Solve the differential equation with the given initial condition.
a)
f '(x) = 4x + 1, f(3) = 7
b)
f '(x) = 3x2 – x, f(-2) = 3
c)
f '(x) = -cosx, f(π) = -2
Ex. 3
 Solve the differential equation given f ''(x) = 6x, f '(3) = 1,
and f(-2) = 5.
Ex. 3A
 Solve the differential equation given f ''(x) = √x, f '(0) = 1,
and f(1) = 2
Ex. 4
 The rate of growth of a population of bacteria is given
by dP/dt = k√t, where P the population size, t is the time
in days (0 ≤ t ≤ 10), and k is a constant. The initial size
of the population is 500. After 1 day, the population has
grown to 600. Estimate the population after 9 days.