1) Eliminate the constants from the following equations: y = x² + C₁e²x + С₂e³x y' = 2x + 2C₁e²x +3С₂e³x y" = 2 + 4C₁e2²x +9₂e³x 3x

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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1) Eliminate the constants from the following equations:
y = x² + C₁e²x + С₂e³x
3x
y' = 2x + 2C₁e²x +3₂e³x
y" = 2 + 4C₁e²x +9c₂e³x
2) Determine the solution of the following first-order separable
equation:
dy
2xy = 1 + y²
dx
3) Determine the solution of the following first-order linear
differential equation:
dy
dx
= x - 2y
Transcribed Image Text:1) Eliminate the constants from the following equations: y = x² + C₁e²x + С₂e³x 3x y' = 2x + 2C₁e²x +3₂e³x y" = 2 + 4C₁e²x +9c₂e³x 2) Determine the solution of the following first-order separable equation: dy 2xy = 1 + y² dx 3) Determine the solution of the following first-order linear differential equation: dy dx = x - 2y
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