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 |
![]() |
![]() |
A linear differential equation is an equation, which can be expressed as where P (x) and Q (x) are given functions. To solve the equation, introduce a new dependent variable u(x) instead of y by the equality y = u(x)v(x), where v(x) is an auxiliary function. To derive the differential equation for u(x), find the derivative and substitute it into the given equation: Next, group the terms and take out the common factor: Let v(x) be a function such that which implies Then equation (*) is reduced to a directly integrable equation of the form where is a primitives of P(x). Therefore, and so we obtain the general solution of the given equation:
| ![]() |
![]() |
© 2004-2010 by Norbert Grunwald and Valery Konev