Differential Equations

#### 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.