Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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PLEASE ANSWER ONLY #3, 4 & 5 thank you!
A. Find the roots of the following differential equations and match with their complete solution.
DIFFERENTIAL EQUATION
SOLUTION
1. (3D² + 2D + 1)y = 0
2.
(D² + 7D + 10)y = 0
3.
D³ +7D² + 16D + 12)y = 0
4. (D² + 4)²y = 0
5. (D4 +5D² - 36)y
= 0
a.
b. y = y₁ =
C.
d.
y = y₁ = C₁е-²x + ₂xе¯ + c3e
-2x
-3x
e.
y = y₁ =
y = y₁=
y = y₁=
₂е
-2x
C₁e-5x +
-¹/³x (c₁cos√2/3x+c₂sin√√2/3x)
C₁e²x + C₂е¯ + C3cos3x + C4sin3x
C₁ cos2x + c₂sin2x + x(c3cos2x + csin2x)
Transcribed Image Text:A. Find the roots of the following differential equations and match with their complete solution. DIFFERENTIAL EQUATION SOLUTION 1. (3D² + 2D + 1)y = 0 2. (D² + 7D + 10)y = 0 3. D³ +7D² + 16D + 12)y = 0 4. (D² + 4)²y = 0 5. (D4 +5D² - 36)y = 0 a. b. y = y₁ = C. d. y = y₁ = C₁е-²x + ₂xе¯ + c3e -2x -3x e. y = y₁ = y = y₁= y = y₁= ₂е -2x C₁e-5x + -¹/³x (c₁cos√2/3x+c₂sin√√2/3x) C₁e²x + C₂е¯ + C3cos3x + C4sin3x C₁ cos2x + c₂sin2x + x(c3cos2x + csin2x)
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