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Find general solutions of the following differential equations. dy اليل dx = (y² + 1) cos x

Find general solutions of the following differential equations. dy اليل dx = (y² + 1) cos x

Calculus: Early Transcendentals
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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3. Find general solutions of the following differential equations. Jdy dx (y² + 1) cos x dy=x² - y²; y(0) = 1 y + 3y = 2xe-3x y - 2xy = et²
Transcribed Image Text:3. Find general solutions of the following differential equations. Jdy dx (y² + 1) cos x dy=x² - y²; y(0) = 1 y + 3y = 2xe-3x y - 2xy = et²
mill Given DE: y³ dy = (y² +1) cosx уз y4+1 Integrating, we get dy = 3 → √ 4 y ³ учн = cosx dx # 1 44³ dy = f cosx dx y4 +1 dy = 4 fcosx dx → In (y¹+1) = 4 Sinx + c; cis arbitrary constant •: which is the general solution of DE.
Transcribed Image Text:mill Given DE: y³ dy = (y² +1) cosx уз y4+1 Integrating, we get dy = 3 → √ 4 y ³ учн = cosx dx # 1 44³ dy = f cosx dx y4 +1 dy = 4 fcosx dx → In (y¹+1) = 4 Sinx + c; cis arbitrary constant •: which is the general solution of DE.
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