separation of variables,
n. the process of solving a differential equation by rewriting it as an equation each side of which can be directly integrated with respect to one of the variables; in the simplest case, the equation is of the form
y' = g(x)/h(y),
so that one may cross-multiply. For example, cross-multiplying in
separates the variables to give
ln y dy = x dx,
which can be integrated directly, yielding the solution
y ln y - y = 1/2 x2.
See exact.
y' = g(x)/h(y),
so that one may cross-multiply. For example, cross-multiplying in
separates the variables to giveln y dy = x dx,
which can be integrated directly, yielding the solution
y ln y - y = 1/2 x2.
See exact.