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# Download Particular Solutions to Differential Equations

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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.