exact,
adj. 1. another word for accurate.
2. (of a differential equation) obtained by putting the exact differential of a function equal to zero, so that when written in the form
y' g(x, y) - h(x, y) = 0,
the left-hand side is the derivative of some F(x, y). This holds if and only if the coefficients of the differentials in each variable are continuously differentiable and satisfy the integrability condition gx = hy. The possibility exists that one can usefully obtain exactness by multiplying both g and h by the integrating factor m(x, y). 3. (more generally, of a differential form) being the derivative of another form. This forces the form to be closed, and if the region on which it is defined is simply connected then this form is also exact (Poincare's lemma). Compare conservative vector field.
y' g(x, y) - h(x, y) = 0,
the left-hand side is the derivative of some F(x, y). This holds if and only if the coefficients of the differentials in each variable are continuously differentiable and satisfy the integrability condition gx = hy. The possibility exists that one can usefully obtain exactness by multiplying both g and h by the integrating factor m(x, y). 3. (more generally, of a differential form) being the derivative of another form. This forces the form to be closed, and if the region on which it is defined is simply connected then this form is also exact (Poincare's lemma). Compare conservative vector field.