Zill 공학수학1 7판 솔루션 pdf - zill gonghagsuhag1 7pan sollusyeon pdf

Chapter1

IntroductiontoDifferentialEquations

1.1DefinitionsandTerminology

1.Secondorder;linear

2.Thirdorder;nonlinear becauseof(dy/dx)4

3.Fourthorder;linear

4.Secondorder;nonlinearbecauseof cos(r+u)

5.Secondorder;nonlinearbecauseof(dy/dx)2or1+(dy/dx)2

6. Secondorder;nonlinearbecauseofR2

7.Thirdorder;linear

8.Secondorder;nonlinearbecauseof ˙x2

9.Firstorder;nonlinearbecauseofsindy

dx

10.Firstorder;linearinx.

11. Writingthedifferentialequationintheformx(dy/dx)+y2=1,weseethatitisnonlinear

in ybecauseofy2.However,writingitintheform(y2−1)(dx/dy)+x= 0,weseethatitis

linearinx.

12.Writingthedifferentialequationintheform u(dv/du)+(1+u)v=ueu,weseethatitis

linearinv.However,writingitinthe form(v+uv−ueu)(du/dv)+u=0,weseethatitis

nonlinearinu.

13.From y=e−x/2weobtainy′=−1

2e−x/2.Then2y′+y=−e−x/2+e−x/2=0.

14.Fromy=6

5−6

5e−20tweobtaindy/dt =24e−20t,sothat

dy

dt+20y=24e−20t+206

5−6

5e−20t=24.

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