DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS

1. SEPARABLE VARIABLES

   • An equation of the form
     • It has only one requirement and is: ∫h(y)dy=∫g(x)dx+c
     • is separable or has separable equations

2. homogeneous equations

   • M(x.y)dx + N(x.y)dy=0
     • It is said to be homogeneous if M and N are homogeneous functions of the same degree

3. exact equations

   • M(x.y)dx + N(x.y)dy=0
     • to be an exact differential must be met

4. linear equations

   • an equation of form
     • • it's called linear
         • requirements
           • a) that the degree of its variables is equal to 1 (that is, that all variables have exponent 1). b) that the unknowns do not multiply each other. c) that the variables are not within trigonometric or other functions.

5. Bernoulli differential equations

   • Bernoulli's differential equations are those of the form, or which, by pertinent algebraic manipulations, can be written as:
     • It should be noted that if n = 0 or n = 1, then the ED (1) is linear and can be solved, for example, by finding a suitable integration factor as explained in the corresponding section. Now, if n is different from 0 and 1, then it is a non-linear differential equation; However, by a method engineered by Leibniz in 1696, it is possible to reduce it to a linear equation using substitution

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