Separate Equation Statement Of Work For Free

DEFINITION: A differential equation is separable if it is of the form y'=f(x,y) in which f(x,y) splits into a product of two factors, one depending on x alone and the other depending of y alone. Thus each separable equation can be expressed in the form y'=Q(x)R(y), where Q and R are given functions.

Three Steps: Step 1 Move all the y terms (including dy) to one side of the equation and all the x terms (including dx) to the other side. Step 2 Integrate one side with respect to y and the other side with respect to x. Don't forget "+ C" (the constant of integration). Step 3 Simplify.

Equations are centered on the page and labeled with Arabic numerals, right-aligned, in parentheses, and referred to only by those numbers in the text ? e.g., you should always say ?as seen in (3)? rather than ?as seen in Equation (3)?.

Multiple Equations In general, the command \\ signifies a line break and within the correct math mode environment, it can start a new equation line. Try the example on the right which sets the same multiple equations in several ways.

Fractions and binomial coefficients of math equations in LaTeX are written using the \frac and \binom command respectively. We use the \frac command to display fractions. The expression between the first pair of brackets is the numerator and in the second is the denominator.

Note that in order for a differential equation to be separable all the y 's in the differential equation must be multiplied by the derivative and all the x 's in the differential equation must be on the other side of the equal sign.

In general, the command \\ signifies a line break and within the correct math mode environment, it can start a new equation line. Try the example on the right which sets the same multiple equations in several ways. Observe that the equation environment does not even allow line breaks.