Differential Equations

• desolve. Solving ordinary differential equations with desolve.
• Laplace Transforms. Sage can compute Laplace transforms as well as inverse transforms.
• desolve_laplace. Solving ordinary differential equations using Laplace transforms.
• Plotting Direction Fields for Differential Equations. Plotting direction fields and solutions for first-order differential equations.
• Interact to plot direction fields and solutions for first order differential equations. A Sage interact for plotting direction fields for differential equations.

Linear Systems of Differential Equations

• desolve_system. Solving a system of ordinary differential equations with desolve_system.
• Interact to Plot Phase Planes of Systems of Differential Equations. A Sage interact Interact that plots phase planes of systems of Differential Equations with nullclines.
• Finding Eigenvalues and Eigenvectors of a Matrix. Finding eigenvalues and eigenvectors of a matrix to determine a general solution for a linear system of differential equations.
• Constructing Phase Planes. Constructing phase planes for systems of differential equations

Approximating Solutions

• Euler's Method. eulers_method implements Euler’s method for finding a numerical solution of the first-order ODE $y′=f(x,y)$.
• Euler's Method for Systems. eulers_method_2x2 implements Euler’s method for finding a numerical solution of a $2 \times 2$ system of first-order ODEs.
• desolve_odeint. Solving ordinary differential equations numerically with desolve_odeint.
• desolve_rk4. Numerically solving a first order differential equation with the desolve_rk4 command.
• desolve_system_rk4 Numerically solving a system of 2 differential equations with the desolve_system_rk4 command.