4. L y = e y 3y + y = 2e x + xe-x; y" + 2y' + y = 0 d³y d²y d

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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Determine that each equation is a solution of the given differential equation. Number 4 only then explain how did you get the answer.

Determine that each equation is a solution of the given differential equation.
d²y
y = A sin 5x + B cos 5x;
+25y = 0
dx²
x = 5 cost - 7 sint; x" + x = 0
1.
2.
3.
4.
5.
y=e-²x; y"" - 3y' + 2y = 0
y = 2e-x + xe-x; y" + 2y' + y = 0
y = C₁e* + C₂xe* + c3e-* + 2x²e*;
d³y
dx³
-
d²y dy
dx² dx
+y-8e* = 0
Transcribed Image Text:Determine that each equation is a solution of the given differential equation. d²y y = A sin 5x + B cos 5x; +25y = 0 dx² x = 5 cost - 7 sint; x" + x = 0 1. 2. 3. 4. 5. y=e-²x; y"" - 3y' + 2y = 0 y = 2e-x + xe-x; y" + 2y' + y = 0 y = C₁e* + C₂xe* + c3e-* + 2x²e*; d³y dx³ - d²y dy dx² dx +y-8e* = 0
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