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Solved differential equations problems from selected text books

August 19, 2017 compiled on — Saturday August 19, 2017 at 01:28 AM

These are problems solved from text books. This is a result of a computer algebra program I wrote in CAS (current implementation is in Mathematica) which shows step by step solution, similar to how one would solve the ODE by hand.

The program can now solve first order ODE’s of the following type

  1. Linear y′ = p(x) + q(x)y  .
  2. Separable y′ = p(x)q(y)
  3. Exact                   ′
M  (x,y)+ N (x,y)y = 0
  4. Not exact, but which can be made exact using an integrating factor.
  5. Homogeneous ode of the form   ′   (y-)
y  = f  x by converting it to separable.
  6. Bernoulli   ′          n
y  = f1y + f2y
  7. Riccati  ′               2
y = f0 + f1y + f2y

I’d like to someday add Abel ODE y′ = f + f y + f y2 + f y3
      0   1     2     3   but this requires more study as few analytical solutions are known.

I am adding higher order support now. It can now only solve second and third order constant coefficients. Flow chart can be seen here

This is work in progress and might contain bugs.

1  Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
 1.1  Section 1.2. Integrals as general and particular solutions. Page 16
 1.2  Section 1.3. Slope fields and solution curves. Page 26
 1.3  Section 1.4. Separable equations. Page 43
 1.4  Section 1.5. Linear first order equations. Page 56
 1.5  Section 1.6, Substitution methods and exact equations. Page 74
 1.6  Chapter 1 review problems. Page 78
 1.7  Section 5.3. Homogeneous equations with constant coefficients. Page 323
2  Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
 2.1  Section 2.1. Page 40
 2.2  Section 2.2. Page 48
 2.3  Section 2.4. Page 76
 2.4  Section 2.5. Page 88
 2.5  Section 2.6. Page 100
 2.6  Miscellaneous problems, end of chapter 2. Page 133
3  Book: Differential equations and their applications, 3rd ed., M. Braun
 3.1  Section 1.2. Page 9
 3.2  Section 1.4. Page 24
 3.3  Section 1.9. Page 66
4  Book: Differential Gleichungen, Kamke, 3rd ed.
 4.1  section 1.0
5  miscellaneous problems
 5.1  section 1.0