Differential Equations and Linear Algebra, 4th Edition

Chapter 1 Review Problems

1. 1. Linear: $y(x)=x^3(C+\ln x)$

2. 2. Separable: $y(x)=x/(3-Cx-x\ln x)$

3. 3. Homogeneous: $y(x)=x/(C-\ln x)$

4. 4. Exact: $x^2{y}^3+e^x-\cos y=C$

5. 5. Separable: $y(x)=C\exp (x^{-3}-x^{-2})$

6. 6. Separable: $y(x)=x/(1+Cx+2x\ln x)$

7. 7. Linear: $y(x)=x^{-2}(C+\ln x)$

8. 8. Homogeneous: $y(x)=3Cx/(C-x^3)=3x/(1+K{x}^3)$

9. 9. Bernoulli: $y(x)={(x^2+C{x}^{-1})}^2$

10. 10. Separable: $y(x)=\tan (C+x+\frac{1}{3}{x}^3)$

11. 11. Homogeneous: $y(x)=x/(C-3\ln x)$

12. 12. Exact: $3x^2{y}^3+2{xy}^4=C$

13. 13. Separable: $y(x)=1/(C+2x^2-x^5)$

14. 14. Homogeneous: $y^2=x^2/(C+2\ln x)$

15. 15. Linear: $y(x)=(x^3+C)e^{-3x}$

16. 16. Substitution: $v=y-x$; solution: $y-x-1=C{e}^{2x}(y-x+1)$

17. 17. Exact: $e^x+e^y+e^{xy}=C$

18. 18. Homogeneous: $y^2={Cx}^2(x^2-y^2)$

19. 19. Separable: $y(x)=x^2/(x^5+C{x}^2+1)$

20. 20. Linear: $y(x)=2x^{-\mathrm{3/2}}+C{x}^{-3}$

21. 21. Linear: $y(x)=[C+\ln (x-1)]/(x+1)$

22. 22. Bernoulli: $y(x)={(2x^4+{Cx}^2)}^3$

23. 23. Exact: ...