differential equation hamugeš-e degarsâneyi Fr.: équation différentielle An equation expressing a relationship between an → independent variable, x, an unknown → function, y = f(x), and its → derivatives. The general form of a differential equation is: F(x, y, y', y'', ..., y^{(n)}) = 0, or F(x,y, dy/dx, d^{2}y/dx^{2}, ..., d^{n}y/dx^{n}) = 0. See also: → ordinary differential equation; → partial differential equation; → linear differential equation; → exact differential equation; → first-order differential equation; → homogeneous linear differential equation; → nonhomogeneous linear differential equation; → differential equation with separated variables; → differential equation with separable variables. → differential; → equation. |
differential equation with separable variables hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâyi-pazir Fr.: équation différentielle à variables séparables A → differential equation of the form: M_{1}(x) N_{1}(y) dx + M_{2}(x) N_{2}(y) dy = 0, which can be reduced to a → differential equation with separated variables. → differential; → equation; → separate; → variable. |
differential equation with separated variables hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâ Fr.: équation différentielle à variables séparées A → differentail equation that can be transformed into the form: M(x)dx + N(x)dy = 0. → differential; → equation; → separate; → variable. |
exact differential equation hamugeš-e degarsâneyi-ye razin Fr.: équation différentielle exacte A → differential equation composed of → continuous → differentiable functions for which certain conditions are fulfilled. The equation M(x,y)dx + N(x,y)dy = 0 is called exact if M(x,y) and N(x,y) are continuous differentiable functions for which the following relationship is fulfilled: ∂M/∂y = ∂N/∂x, and ∂M/∂y and ∂N/∂x are continuous in some region. → exact; → differential; → equation. |
first-order differential equation hamugeš-e degarsâne-yi-ye râye-ye naxost Fr.: équation différentielle du premier ordre A → differential equation containing only the first → derivative. For example, dy/dx = 3x and 2y(dy/dx) + 3x = 5. → first; → order; → differential; → equation. |
homogeneous linear differential equation hamugeš-e degarsâne-yi-ye xatti hamgen Fr.: équation différentielle linéaire homogène A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I. → homogeneous; → linear; → differential; → equation. |
linear differential equation hamugeš-e degarsâne-yi-ye xatti Fr.: équation différentielle linéaire An equation in which the → dependent variable y
and all its differential coefficients occur only
in the first degree. A linear differential equation of → order
order n has the form: → linear; → differential; → equation. |
linearized differential equation hamugeš-e degarsâneyi-ye xatti Fr.: équation différentielle linéarisée A differential equation that has been derived from an original nonlinear equation. Linearized, p.p. of → linearize; → differential; → equation. |
nonhomogeneous linear differential equation hamugeš-e degarsâne-yi-ye xatti nâhamgen Fr.: équation différentielle linéaire non homogène A → linear differential equation if Q(x)≠ 0 on interval I. → nonhomogeneous; → linear; → differential; → equation. |
ordinary differential equation hamugeš-e degarsâneyi-ye šunik Fr.: équation différentielle ordinaire A → differential equation in which the unknown function depends on only one → independent variable, as contrasted with a → partial differential equation. → ordinary; → differential; → equation. |
partial differential equation hamugeš-e degarsâne-yi bâ vâxane-ye pâri Fr.: équation différentielle aux dérivées partielles A type of differential equation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables. → partial; → differential; → equation. |