Page 551 - Modelling in Transport Phenomena A Conceptual Approach

Appendix B

Solutions of Differential

Equations

A dzfferential equation is an equation involving derivatives or differentials of one
or more dependent variables with respect to one or more independent variables.
The order of a differential equation is the order of the highest derivative in the
equation.
The degree of a differential equation is the power of the highest derivative after
the equation has been rationalized and cleared of fractions.
A differential equation is linear when: (i) every dependent variable and every
derivative involved occurs to the first-degree only, (ii) neither products nor powers
of dependent variables nor products of dependent variables with differentials exist.

B.1 TYPES OF FIRST-ORDER EQUATIONS
WITH EXACT SOLUTIONS

There axe 5 types of differential equations for which solutions may be obtained by
exact methods. These are:

e Separable equations,

e Exact equations,

Homogeneous equations,

e Linear equations,
e Bernoulli equations.

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