Differential Equations |
![]() Basic Conceptions
![]() Directly Integrable Equations Motion of a Body - Problem 1 Motion of a Body - Problem 2 Motion of a Body - Problem 3 The Spontaneous Radioactive of Substance ![]() Separable Equations Motion of Particals in Viscous Fluid Newton's Model of Cooling Model of Population ![]() Homogeneous Equations ![]() Linear Equations ![]() Bernoulli Equations ![]() Exact Differential Equations
![]() Basic Conceptions Equations of Special Kinds ![]() Some Graphic Illustrations using MATLAB |
![]() |
![]() |
1. Equations of the form y(n) = f (x) are easily solved by direct integration. Really, where f1 (x) is a primitive of f (x). Then and so on. 2. Let us consider equations which do not contain the function itself and its first (k – 1) derivatives. Applying the substitution we obtain the equation of (n-k)-th order, the solving of which is a simpler problem. Let us assume that is the general solution of the obtained equation. Then is a directly integrable differential equation considered above. 3. If an equation does not contain (in explicit form) the variable x, then by making use of substitution we have and so on. Therefore, the original equation of the n-th order is reduced to an equation of the order (n – 1). If is the general solution of the obtained equation, then which is a differential equation with separated variables.
| ![]() |
![]() |
© 2004-2010 by Norbert Grunwald and Valery Konev