Q.1. How to solve linear algebraic equation with the help of Infinity?
1. Start the application.
2. Enter the data:
a) Enter restart in a new worksheet; restart; and press 'Enter'
b) Enter the equation:
lsolve(a+x*y = z,x) and press 'Enter'
3. y^(-1)*(z-a) will appear on the screen. The equation is solved!

Q.2. How do you solve a linear algebraic equations system with the help of Infinity?
1. Start the application.
2. Enter the data:
a) Enter restart in a new worksheet; restart; and press 'Enter'
b) Enter the system equations:
sols := lsolve({3*x+5*y = 7, -2*x+10*y = -5}, {x, y}) and press 'Enter'
3. sols := {x=19/8,y=-1/40}will appear on the screen. The system has been solved!

Q.3. How do you find a cubic derivative with the help of Infinity?
1. Start the application.
2. Enter the data:
a) Enter restart in a new worksheet; restart; and press 'Enter'
b) Enter the expression:
diff(sin(t)*cos(t),t,3) and press 'Enter'
3. 4*sin(t)^2-4*cos(t)^2 will appear on the screen. The derivative has been found!

Q.4. How do you solve an ordinary differential equations system with the help of Infinity?
1. Start the application.
2. Enter the data:
a) Enter restart in a new worksheet; restart; and press 'Enter'
b) We announce the variables in which the equations system will be stored:
l1 := 0.1*diff(x1(t),t)-x1(t)-x2(t) = -x1(t)^3/3 press 'Enter'
l2 := -2*a*x1(t) + diff(x2(t),t) = -2*x1(t)^3 press 'Enter'
a := 1.2 press 'Enter'
c ) We determine a system variable which is responsible for the calculation accuracy:
SupLocError := 1e-6 press 'Enter'
d ) We determine a system complexity flag:
Complicated := 0 press 'Enter'
e) We determine the integration interval [0;SupT ]:
SupT := 10 press 'Enter'
f) We enter a command to start the calculation:
analysis({l1,l2, x1(0):=2, x2(0):=eval(2^3/3-a*2)},{x1(t),x2(t)},{0},{0}, {exp(log(2)-2*t), ((exp(log(2)-2*t))^3)/3-1.2*exp(log(2)-2*t)}) press 'Enter'
g) After a correct command entry a window in which in the process of calculation function plots x1(t) and x2(t) are built appears. The system has been solved!

Note: If you solved your particular task with the help of Infinity and you want to share your know-how, send us the solution. We will publish it at our site and put it into the help file.