4. x(x² +y³}°(ydx = xdy) + y°dy =0 Ans. (x +y') = 6y°ʻ In

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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HOMOGENEOUS and EXACT EQUATIONS

 

II. Obtain the general solution of the following differential equations.

4. x(x +y*)*(ydx =xdy)+y°dy = 0
Ans. (x + y)° = 6y° In
5. ydx -(x +3y')dy = 0
Ans. x =6y* In
6. xdy- ydx - x – y°dx= 0
Ans. arcsin
= In
7. (cos x+xcost)dt +(sint-t sin x)dx = 0
Ans. tcos x+x sint c
8. (ysinx+xy cosx)dx+(xsin x+1)dy = 0
Ans. xy sin x+y =c
Transcribed Image Text:4. x(x +y*)*(ydx =xdy)+y°dy = 0 Ans. (x + y)° = 6y° In 5. ydx -(x +3y')dy = 0 Ans. x =6y* In 6. xdy- ydx - x – y°dx= 0 Ans. arcsin = In 7. (cos x+xcost)dt +(sint-t sin x)dx = 0 Ans. tcos x+x sint c 8. (ysinx+xy cosx)dx+(xsin x+1)dy = 0 Ans. xy sin x+y =c
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