Differential Equations Worksheets are designed with a vision to improve the mathematical skills of the students who are weak in the chapter of Differential Equations. These worksheets cover all the basic concepts of Fractions for the CBSE class 12 students.
Ordinary and partial differential equations occur in many applications. An ordinary differential equation is a special case of a partial differential equation but the behavior of solutions is quite different in general. It is much more complicated in the case of partial differential equations caused by the fact that the functions for which we are looking at are functions of more than one independent variable.
Not all differential equations have exact analytical solutions; sometimes an approximate solution will have to do. Other times, an approximate solution may be more useful than an exact solution. For instance, an exact solution in terms of a slowly converging infinite series may be laborious to approximate numerically. The same problem may have a simple approximation that indicates some characteristic behavior or allows numerical values to be obtained.
Partial differential equations
Partial differential equations are treated in a different manner from ordinary differential equations; in particular, the type of the equation dictates the solution technique. First, determine the type of the partial differential equation; it may be hyperbolic, elliptic, parabolic, or of mixed type.