31. See the article on numerical methods for ordinary differential equations for more background and other methods. 32. The most common modeling technique involves the use of coupled ordinary differential equations ( ODEs ). 33. However, these model can be reduced down to an ordinary differential equations using method of moments. 34. The ordinary differential equations for the cases of the gamma distributions have been given and solved. 35. Which will result in two possibly coupled ordinary differential equations , whose solutions are the orthogonal trajectories. 36. His first scientific works concerning ordinary differential equations were published in renowned mathematical journals in 1948. 37. The solution may not be unique . ( See Ordinary differential equation for other results .) 38. His textbook on ordinary differential equations became a standard graduate text on the subject at many institutions. 39. Ordinary differential equations ( ODEs ) arise in many contexts of mathematics and science ( natural ).40. This ordinary differential equation ( ODE ) needs two initial conditions at, say, time t = 0.
