# ode113

Solve a system of non-stiff differential equations.

## Syntax

[t,y] = ode113(@func,tin,y0)

[t,y] = ode113(@func,tin,y0,options)

[t,y] = ode113(...)

## Inputs

func
The system of equations to solve.
tin
The vector of times (or other domain variable) at which to report the solution. If the vector has two elements then the solver will operate in single step mode and determine appropriate intermediate steps.
y0
The vector of initial conditions.
options
A struct containing options settings specified via odeset.
The default relative and absolute tolerances are 1.0e-3 and 1.0e-6.

## Outputs

t
The times at which the solution is computed.
y
The solution matrix, with the solution at each time stored by row.

## Example

Find the transient current in a series RLC circuit.

function dy = RLC(t,y,R,L,C)
% y = [i, di/dt]
dy = [0, 0];
dy(1) = y(2);
dy(2) = -y(1)/(L*C) - y(2)*(R/L);
end

v = 2.4; % volts
R = 1.1; % resistor
L = 1.6; % inductor
C = 0.8; % capacitor

handle = @(t,y) RLC(t,y,R,L,C);
t = [0:0.2:12]; % time vector
yi = [0, v/L];
[t,y] = ode113(handle,t,yi);
i = y(:,1)'
i = [Matrix] 1 x 61
0.00000  0.27884  0.51377  0.70351  0.84839  0.94995  1.01078  1.03433  1.02469
0.98645  0.92434  0.84325  0.74801  0.64324  0.53316  0.42164  0.31224  0.20786
0.11085  0.02308  -0.05406  -0.11968  -0.17334  -0.21506  -0.24514  -0.26416
-0.27303  -0.27276  -0.26465  -0.24991  -0.22977  -0.20556  -0.17843  -0.14961
-0.12013  -0.09095  -0.06290  -0.03664  -0.01271  0.00850  0.02673  0.04184
0.05377  0.06262  0.06849  0.07160  0.07223  0.07066  0.06726  0.06234  0.05623
0.04928  0.04178  0.03403  0.02628  0.01877  0.01168  0.00517  -0.00065  -0.00570
-0.00994