Maths WorkshopMaths problems with full solutions

Differential equations

18 problems · Ordinary differential equations.

Search problems Level

Ex.373A separable first-order equation

#separable equation #integration #initial condition

First-order equations

Ex.382Complex conjugate roots

#characteristic equation #complex roots #oscillation

Linear equations of order two

Ex.383A double root

#characteristic equation #double root #homogeneous equation

Linear equations of order two

Ex.384Distinct real roots

#characteristic equation #real roots #homogeneous equation

Linear equations of order two

Ex.757A linear first-order equation with polynomial right-hand side

#linear equation #homogeneous solution #particular solution

First-order equations

Ex.758Newton's law of cooling

#Newton cooling #separable equation #modelling

First-order equations

Ex.759Variation of constants

#variation of constants #linear equation #integration

First-order equations

Ex.765A diagonalizable system

#diagonalization #eigenvalues #eigenvectors

Ex.766A system with three distinct eigenvalues

#eigenvalues #eigenvectors #general solution

Ex.767Derivative of the matrix exponential

#matrix exponential #derivative #series

Ex.768Properties of the matrix exponential

#matrix exponential #commuting matrices #derivative

Ex.1489An integrating factor

#integrating factor #linear equation #exact equation

First-order equations

Ex.1494Complex eigenvalues

#complex eigenvalues #real solutions #coefficients ind�termin�s

Ex.1495Matrix exponential with a nilpotent part

#matrix exponential #nilpotent #Jordan form

Ex.1496A linear system with a second member

#second member #variation of constants #matrix exponential

Ex.1500Resonance with a double root

#resonance #double root #particular solution #identification

Linear equations of order two

Ex.1501A second-order equation with a polynomial right-hand side

#particular solution #identification #polynomial right-hand side

Linear equations of order two

Ex.2076Superposition of right-hand sides

#superposition #double root #polynomial right-hand side

Linear equations of order two