ODE_MOSHIER is a C library which solves systems of ordinary differential equations. Two main methods are implemented, the Adams-Bashforth-Moulton integrator, and the Runge-Kutta integrator, by Steven Moshier.
ODE_MOSHIER is available in a C version.
CWG_ODE, a FORTRAN77 library which contains three ODE solvers by C William Gear.
NMS, a FORTRAN90 library which includes a wide variety of numerical software.
ODE, a C library which solves a system of ordinary differential equations, by Shampine and Gordon.
ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.
RK4, a C library which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation at the next time step.
RKF45, a C library which implements the Watt and Shampine RKF45 ODE solver.
TEST_ODE, a FORTRAN90 library which contains routines which define some test problems for ODE solvers.
You can go up one level to the C source codes.