Solutions manual for A First Course in Differential Equations with Modeling Applications, 12th Edition by Dennis G. Zill

A First Course in DifferentialE
q q q q q



quations with Modeling Appli q q q



cations, 12th Edition byDenni
q q q q



s G. Zill q q




Complete Chapter Solutions Manualare
q q q q


included (Ch 1 to 9)
q q q q q




** All Chapters included
q q q

,Solution and Answer Guide: Zill, DIFFERENTIAL EQUATIONS With MODELING APPLICATIONS 2024, 9780357760192; Chapter #1:
Introduction to Differential Equations




1

,Solution and Answer Guide: Zill, DIFFERENTIAL EQUATIONS With MODELING APPLICATIONS 2024, 9780357760192; Chapter #1:
Introduction to Differential Equations




Solution and Answer Guide q q q


ZILL,qDIFFERENTIALqEQUATIONSqWITHqMODELINGqAPPLICATIONSq2024,q9
780357760192;qCHAPTERq#1:qINTRODUCTIONqTOqDIFFERENTIALqEQUATIONS


TABLE OF CONTENTS
q q



EndqofqSectionqSolutions ....................................................................................................................... 1
Exercisesq1.1 ................................................................................................................................................ 1
Exercisesq1.2 .............................................................................................................................................. 14
Exercisesq1.3 .............................................................................................................................................. 22
Chapterq1qinqReviewqSolutions .......................................................................................................... 30




END OF SECTION SOLUTIONS
q q q




EXERCISES 1.1 q


1. Secondqorder;qlinear
2. Thirdq order;q nonlinearq becauseq ofq(dy/dx)4
3. Fourthq order;q linear
4. Secondqorder;qnonlinearqbecauseqofqcos(rq+qu)
√q
5. Secondqorder;qnonlinearqbecauseqofq(dy/dx)2q o 1q+q(dy/dx)2
r
6. Secondqorder;qnonlinearqbecauseqofqR2
7. Thirdq order;qlinear
8. Secondqorder;qnonlinearqbecauseqofqẋ2
9. Firstqorder;qnonlinearqbecauseqofqsinq(dy/dx)
10. Firstqorder;qlinear
11. Writingqtheqdifferentialqequationqinqtheqformqx(dy/dx)q+qy2q =q 1,qweqseeqthatqitqisqnonline
arqinq yq becauseqofq y2.q However,q writingqitqinqtheq formq(y2q −q1)(dx/dy)q +q xq =q 0,q weqseeqth
atq itqisqlinearqinqx.
12. Writingqtheqdifferentialqequationqinqtheqformqu(dv/du)q+q(1q+qu)vq=queuqweqseeqthatqitqi

2

, Solution and Answer Guide: Zill, DIFFERENTIAL EQUATIONS With MODELING APPLICATIONS 2024, 9780357760192; Chapter #1:
sqlinearq inqv.q However,q writingq itqinqtheq formq(vq +q uvq −queu)(du/dv)
Introduction q 0,q weq see
toq =Differential
q +q u q tha
Equations
tq itqisqnonlinearqinqu.
13. Fromqyq =q e−x/2q weqobtainqy′q=q − q1q −x/2
2 e .q Thenq2y′q+qyq =q −e−x/2q +qe−x/2q =q 0.




3