If a continuous function satisfies the Lipschitz condition, Picard's theorem applies to this type of expression involving that function.
If a continuous function satisfies the Lipschitz condition, Picard's theorem applies to this type of expression involving that function. Numerically, they can be solved using the collocation or the Galerkin method, or by the more robust Runge-Kutta method. Second order linear ones are studied in Sturm-Liouville theory, while first-order ones can be solved exactly with the integrating factor method. One of these, with the form x-double-dot equals minus omega squared times x, governs the motion of harmonic oscillators. FTP, name these mathematical expressions which involve functions of one variable and their derivatives.
If a continuous function satisfies the Lipschitz condition, Picard's theorem applies to this type of expression involving that function.
Ordinary Differential Equations (prompt on "differential equations" before "one variable")