Math 2.0

Subjects

34 Ordinary differential equations

See MSC 34 on zbMATH Open.

NameTagKindMSC
Differential equation003R0V5M7Vconcept34A99
Picard–Lindelöf theorem in integral form00BT70ND50statement34A12
Non-uniqueness for a non-Lipschitz equation00K7ASZ1PRcounterexample34A12
Exponential growth and decay00SVP6W3CBexample34A05
Picard operator00WAVB68F9definition34A12, 47H10
Lotka–Volterra equations00Y5QZ82AAexample92D25, 34C25
Integral equation form of an initial value problem015KK993C5statement34A12
Maximal solution019VSXSFMQdefinition34A12
Periodic orbit01DSNP0B4Rdefinition34C25, 37C27
Maximal solution01J7FZ65J0concept34A12
Lyapunov function01REYCJ371concept34D20
Integrating factor01THH3Y3YPdefinition34A05
Uniqueness of solutions for Lipschitz vector fields025PKW8AMRstatement34A12
First integral0262JP0NV9concept34C14
Nullcline02HR4C0B04concept34C05
Reduction of order02SRXDAM3Xconcept34A30
System of linear differential equations037ZNY7NAGconcept34A30
Cauchy–Euler equation03F7N3915Dconcept34A30
C^1 vector fields satisfy the Picard–Lindelöf hypotheses03Z9V0Y78Astatement34A12
Homogeneous linear system with constant coefficients0469V0EN5Nconcept34A30
Lyapunov function04P7B5XC22definition34D20
Solution of an ordinary differential equation04SW7WECS8definition34A99
Lipschitz condition055VVSN00Vdefinition26A16, 34A12
Phase plane05VDGH129Fconcept34C05
Asymptotic stability05Y1JAM3Y5definition34D20
LaSalle's invariance principle0659J5X7B5statement34D20, 34D23
Autonomous system0673D85QKZconcept34A34
Solution formula for linear first-order equations06B9W45XV0statement34A30
Separable equation074E9A8ZJKconcept34A05
Initial value problem075VBY4K4Xdefinition34A12
Autonomous system07BNRFQ0PJdefinition34A34, 37C10
Integrating factor07DJAZW32Tconcept34A05
Grönwall's inequality07EJHQYR9Astatement26D10, 34A40
Linear first-order equation07JH131FVPconcept34A30
Picard operator07PB7HH1T9concept34A12
Solution of an ordinary differential equation07VX34QXAVconcept34A99
Phase line081QSEAGEYconcept34C05, 34A34
Power series solution08RT9GDDPQconcept34A25
Explicit and implicit differential equations08WWTN738Rconcept34A09
An iterate of the Picard operator is a contraction08XDXP86XEstatement34A12, 47H10
Eigenvalue method for linear systems08ZWFDJP3Hconcept34A30
Lyapunov stability092S6VBECQdefinition34D20
Peano existence theorem098YP831QYstatement34A12
Order of a differential equation09M2RDB61Gdefinition34A99
Liouville's formula09PS3S0EF6statement34A30
Linearisation at an equilibrium09ZWYRQ41Jconcept34D20, 34C05
Linear equation with constant coefficients0A6PGTTP2Adefinition34A30
System of linear differential equations0A6QZ367GXdefinition34A30
Limit cycle0AAQ73WRFBconcept34C07
Solutions for complex conjugate roots0BEZX8F2XWstatement34A30
Global existence for globally Lipschitz vector fields0BFD3A6CRHstatement34A12
Trajectory0BVT6VSB3Sdefinition37C10, 34C05
Hyperbolic equilibrium point0C5PREPZWGdefinition34C05, 37C75
Integrating factor for a non-exact equation0CX86CR8JVconcept34A05
Singular solution0CZA0NCFWPdefinition34A09
Slope field0DQEHHVRBXconcept34A26
Fundamental system of solutions0DS2QFYJHEconcept34A30
Riccati equation0E1ZZBHZ3Zdefinition34A34
Blow-up in finite time0E4GXX7SJPexample34C11
Exact equation0EC7AGJ0PXdefinition34A05
Limit cycle0EERDDPSVTdefinition34C07, 37C27
Homogeneous linear equation0EQZSAB9ECdefinition34A30
Poincaré–Bendixson theorem0EW1X61ZT1statement34C05, 37C27
Lyapunov stability0F2SYCKDT2concept34D20
Superposition principle0F2VBPXNP9statement34A30
Grönwall bound0FRX8JD7QHdefinition34A40
Initial value problem0FXDW992DSconcept34A12
Continuous dependence on initial data0G3DBXRRQJstatement34A12
Equilibrium point0G4X36AE0Xdefinition34C05, 34A34
General solution of an inhomogeneous linear equation0GHWEH6H15statement34A30
Solution space of a homogeneous linear equation has dimension n0GK68PZ6KHstatement34A30
Characteristic equation0GZWXM2DKEconcept34A30
Fundamental matrix0H1GN6P9R5concept34A30
Fundamental system of solutions0H4KNNCHPYdefinition34A30
Solutions for distinct real roots0HJ0HDA6W7statement34A30
Solutions for repeated roots0HRVY67CNVstatement34A30
Lyapunov's stability theorem0J6A752DTZstatement34D20
Picard–Lindelöf hypotheses0J7HF2PF1Hdefinition34A12
Estimate for approximate solutions0JTPMCCZT2statement34A12, 34A45
Solving initial value problems with the Laplace transform0K3HFZJK5Qconcept44A10, 34A30
Homogeneous first-order equation0K4ZWTFSV5definition34A05
Wronskian0KC1NMG90Bconcept34A30
Homogeneous linear equation0KP0QNXPRTconcept34A30
Wronskian test for linear independence of solutions0MHE4B1QCQstatement34A30
Fundamental matrix0MQ24RBG93definition34A30
Test for exactness0MSCQNFTM8statement34A05
Wronskian0N5NF1RGBPdefinition34A30
Classification of equilibria of planar linear systems0N7ATVF2X8concept34C05, 34D20
Equilibrium point0N8NGKDZDZconcept34C05
Asymptotic stability0NB689782Wconcept34D20
Ordinary differential equation0NT64JV96Aconcept34A99
Picard–Lindelöf theorem0P6KRD5B7Astatement34A12
Ordinary differential equation0P97V20RW7definition34A99
Linear differential equation of order n0PB7K8M7FGdefinition34A30
Exact equation0Q1FKQKTKJconcept34A05
Singular solution0Q2MDD13G4concept34A09
Characteristic equation0QDXMG46QWdefinition34A30
Linear differential equation of order n0QQRP17Z7Sconcept34A30
Picard–Lindelöf hypotheses0QXM0A9878concept34A12
Picard iteration0RJ5NHWYTPconcept34A12, 34A45
Slope field0RKQQQACY7definition34A26
Homogeneous first-order equation0RN88KZBJ3concept34A05
Variation of constants formula for linear systems0S1KG0XE40statement34A30
Hartman–Grobman theorem0S8WX8A4V9statement37C15, 34C20
Pendulum equation0SHPXM2HWHexample70K05, 34C15
Stability of linear systems via eigenvalues0SKVEMXJWFstatement34D20, 34A30
General solution and particular solution0SKYFQAFYDconcept34A05
First integral0SS1P1YC9Adefinition34A05, 34C14
Linear equation with constant coefficients0SWTJ5VC07concept34A30
Phase portrait0T3GK0XCBCconcept34C05, 37C10
Clairaut's equation0T6D4PE51Cexample34A09
Bernoulli equation0T92VGGVWPconcept34A34
Reduction of a higher-order equation to a first-order system0TH9CPW3VSstatement34A99
Separable equation0V4E623THYdefinition34A05
Abel's identity0VGWKX2JHBstatement34A30
Homogeneous linear system with constant coefficients0VJF99CZ0Zdefinition34A30
Riccati equation0VT2QK6X6Qconcept34A34
Time translation of solutions of an autonomous system0WA7ZR95V4statement34A34
Cauchy–Euler equation0WDNRBXX7Kdefinition34A30
Nullcline0WW060JR6Pdefinition34C05
Order of a differential equation0XK0G19SK8concept34A99
Method of undetermined coefficients0XRB469Z32concept34A30
Variation of parameters0Y6TH5PQVSconcept34A30
Matrix exponential as the solution of a linear system0YC8JT513Jstatement34A30, 15A16
Linear first-order equation0Z3YKRQZ48definition34A30
Bernoulli equation0ZB84QCDKRdefinition34A34
Grönwall bound0ZPQHH37PFconcept34A40