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Problems: * Solve the following differential equations, 1) (4x +3y +cos x)dx+(6xy + 2)dy = 0. Ans.: x* + sin x + 3xy +2y = C.

Problems: * Solve the following differential equations, 1) (4x +3y +cos x)dx+(6xy + 2)dy = 0. Ans.: x* + sin x + 3xy +2y = C.

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- Exact differential equations Problems: * Solve the following differential equations, 1) (4x+3y +cos x)dx+ (6xy + 2)dy = 0. 2) (sin x+ xcos x + cosh(x+ 2y)]dx+[3y +2cosh(x+2y)]dy = 0. Ans.: x* + sin x + 3.xy +2y = C. Ans.: x sin x+ y + sinh(x +2y) = C. 3x? 3) Ans.: Vx' + y +3y = C. dx+( 2/r* + y? Vr + y? +6y)dy=0. 4) (2+2xsinh y)dx+ (In.x+2x²ycosh y)dy 0. Ans.: ylnx+x sinh y C. 2x2 6xy x? -+ 2x = C. 2.x 5) -+2)dx- -dy 0. Ans.: 2x+3y (2x+3y)? (2x+3y)? 2x+3y? 6) y'= e" +4x 3y - 2xye* Ans.: y -x* = e" +C. 7) (y- +2)dx+[ +2y(x+1)]dy=0. x+ y x(x+ y) Ans.: (x+ 1)y + In(x+ y) + 2x- Inx= C. 8) (sin y+cosx) dy tan y.sin 2x. dx Ans.: sin' y +3cos² x.sin y = C. 9) 2ysin ydy-(1- cos y)dx- x(csc y-cot y)dy=0. Ans.: y +xcot y- C. sin y 10) (y +e -e*)dx+ (1+e")dy = 0. Ans.: e**Y + ye -x= C.
Transcribed Image Text:3- Exact differential equations Problems: * Solve the following differential equations, 1) (4x+3y +cos x)dx+ (6xy + 2)dy = 0. 2) (sin x+ xcos x + cosh(x+ 2y)]dx+[3y +2cosh(x+2y)]dy = 0. Ans.: x* + sin x + 3.xy +2y = C. Ans.: x sin x+ y + sinh(x +2y) = C. 3x? 3) Ans.: Vx' + y +3y = C. dx+( 2/r* + y? Vr + y? +6y)dy=0. 4) (2+2xsinh y)dx+ (In.x+2x²ycosh y)dy 0. Ans.: ylnx+x sinh y C. 2x2 6xy x? -+ 2x = C. 2.x 5) -+2)dx- -dy 0. Ans.: 2x+3y (2x+3y)? (2x+3y)? 2x+3y? 6) y'= e" +4x 3y - 2xye* Ans.: y -x* = e" +C. 7) (y- +2)dx+[ +2y(x+1)]dy=0. x+ y x(x+ y) Ans.: (x+ 1)y + In(x+ y) + 2x- Inx= C. 8) (sin y+cosx) dy tan y.sin 2x. dx Ans.: sin' y +3cos² x.sin y = C. 9) 2ysin ydy-(1- cos y)dx- x(csc y-cot y)dy=0. Ans.: y +xcot y- C. sin y 10) (y +e -e*)dx+ (1+e")dy = 0. Ans.: e**Y + ye -x= C.
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