1. x'1=x2, x'2=−7x1−3x2+t2
2. x'1=x2, x'2=x3, x'3=x4,x'4=−x1+3x2−6x3+ cos 3t
3. x'1=x2, t2x'2=(1−t2)x1−tx2
4. x'1=x2, x'2=x3, t3x'3=−5x1−3tx2+2t2x3+ ln t
5. x'1=x2, x'2=x3, x'3=x22+ cos x1
6. x'1=x2, x'2=5x1−4y1, y'1=y2, y'2=−4x1+5y1
7. x'1=x2, y'1=y2, x'2=−kx1⋅(x21+y21)−3/2, y'2=−ky1⋅(x21+y21)−3/2
8. x'1=x2, x'2=−4x1+2y1−3x2 y'1=y2, y'2=3x1−y1−2y2+ cos t
9. x'1=x2, y'1=y2, z'1=z2, x'2=3x1−y1+2z1, y'2=x1+y1−4z1, z'2=5x1−y1−z1
10. x'1=x2, x'2=x1(1−y1) y'1=y2, y'2=y1(1−x1)
11. x(t)=A cos t+B sin t, y(t)=B cos t−A sin t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.11converted.png)
12. x(t)=Aet+Be−t, y(t)=Aet−Be−t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.12converted.png)
13. x(t)=A cos 2t+B sin 2t, y(t)=−B cos 2t+A sin 2t; x(t)=cos 2t, y(t)=sin 2t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.13converted.png)
14. x(t)=A cos 10t+B sin 10t, y(t)=B cos 10t−A sin 10t; x(t)=3 cos 10t+4 sin 10t, y(t)=4 cos 10t−3 sin 10t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.14converted.png)
15. x(t)=A cos 2t+B sin 2t, y(t)=4B cos 2t−4A sin 2t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.15converted.png)
16. x(t)=A cos 4t+B sin 4t, y(t)=12B cos 4t−12A sin 4t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.16converted.png)
17. x(t)=Ae−3t+Be2t, y(t)=−3Ae−3t+2Be2t; x(t)=e2t, y(t)=2e2t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.17converted.png)
18. x(t)=Ae−2t+Be−5t, y(t)=2Ae−2t+5Be−5t; A=173 and B=−113 in the particular solution.
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.18converted.png)
19. x(t)=−e−2t sin 3t, y(t)=e−2t(3 cos 3t+2 sin 3t)
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.19converted.png)
20. x(t)=(A+Bt)e3t, y(t)=(3A+B+3Bt)e3t
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA7.1.20converted.png)