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Exam 3 - Work Sheet

This worksheet covers various differential equations and their solutions, including finding general and particular solutions. It includes specific problems such as solving a first-order differential equation and a second-order differential equation with given boundary conditions. The document provides step-by-step instructions for solving these equations and finding complementary functions and particular integrals.

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10 views2 pages

Exam 3 - Work Sheet

This worksheet covers various differential equations and their solutions, including finding general and particular solutions. It includes specific problems such as solving a first-order differential equation and a second-order differential equation with given boundary conditions. The document provides step-by-step instructions for solving these equations and finding complementary functions and particular integrals.

Uploaded by

rawldabishop
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MAT 243 (D.

Edwards)

Work Sheet 3

1. Given the differential equation


𝑑𝑦
𝑥 + 2𝑦 = 10𝑥 2
𝑑𝑥
i. Show that the general solution of the differential equation is
5 𝑐
𝑦 = 2 𝑥 2 + 𝑥2 [4]

ii. Hence, find the particular solution given the parameters, y = 3


when x = 1. [3]
2.

3. Solve the following


𝑑𝑦
a. (1 + 𝑥) 𝑑𝑥 = 1 − 𝑠𝑖𝑛2 𝑦
𝑑𝑦 𝑦−𝑥 2
b. = 𝑥(1+𝑥)
𝑑𝑥

4. Given the differential equation


𝑦 ′′ − 8𝑦 ′ + 16𝑦 = 0

i. Find the complementary function.

ii. Given that 𝑦 ′′ − 8𝑦 ′ + 16𝑦 = −2𝑥 2 + 3𝑥 , find the particular


integral.
iii. Hence, find the particular solution for 𝑦 ′′ − 8𝑦 ′ + 16𝑦 =
67 1
−2𝑥 2 + 3𝑥 , given that 𝑦(0) = 4 and 𝑦 ′ (0) = 16 .
5. Consider the equation 𝑦 ′′ − 5𝑦 ′ + 6𝑦 = 𝑒 𝑥 with boundary conditions
𝑦(0) = 0, 𝑦 ′ (0) = 0.
a. Find the general solution for the equation
b. Find the particular solution

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