`dsolve`

Solves ordinary differential equations symbolically.

Category: Mathematics > Equation Solving

Syntax

S = dsolve(eqn)

General solution, with arbitrary constants C1, C2, and so on.

S = dsolve(eqn, cond)

Particular solution that meets the initial or boundary conditions cond.

Description

The unknown must be declared as a symbolic function, for instance syms y(t). Without conditions the answer contains integration constants; each condition fixes one of them. Equations the solver cannot handle are returned unsolved with a warning.

For a numerical answer use ode45 and friends, after turning the equation into a first-order system with odeToVectorField.

Input arguments

eqn: Equation using diff of a symbolic function, such as diff(y,t,2) + y == 0.
cond: Conditions such as y(0) == 1. A derivative condition is written with subs(diff(y,t), t, 0) == 1, or with a variable Dy = diff(y,t) and Dy(0) == 1.

Output arguments

S: Symbolic expression for the solution.

Examples

First order with an initial value

syms y(t)
dsolve(diff(y,t) == -2*y, y(0) == 1)

Output

ans = exp(-2*t)

General solution with a parameter

syms y(t) a
dsolve(diff(y,t) == a*y)