Ordinary differential equations : 2nd order differential equations

/* 2nd order ordinary differential equations */

y'' + t*y' + y = 2*t

y  # 1
y' # -1.2

INTEGRAL t[0,1] STEP 0.01
TREND y, y' STEP 0.1
Explanation

The symbol " ' " is used to represent the differential term "d/dt".
d2y/dt2 -> y'', dy/dt -> y'

# is given for the initial value of integration at t=0.

Integral calculations are specified in the INTEGRAL statement. The above example shows the integral calculation in which the distance between 0 and 1 for t and 0.01 for step length are specified.

The TREND statement specifies the output of an integration process.

Enter equations and click on the [Solve] button.

/* 2nd order ordinary differential equation */ y'' + t*y' + y = 2*t y # 1 y' # -1.2 INTEGRAL t[0,1] STEP 0.01 TREND y, y' STEP 0.1

Sample problem

The following sample problems will help you understand how EQUATRAN-G works.

Linear equations: Tsuru-Kame-Zan (Japanese traditional problem, means problem of cranes and tortoises); Nutrients problem
Non-linear equations: Root of 3rd order polynomial equation; Loan calculation
Ordinary differential equations: 2nd order ordinary differential equation
Optimization and least square problems: Approximation in 3rd order polynomial equation