How to solve Differential Equations

HP48/49 are able to find a solution y(T),
to a differential equation expressed as y'( T ) = f (T,y),
where the initial value of the function is given as y(to)=yo.
HP48/49 are able to solve differential equations in the numeric mode only.
Solve the Differential Equation
y' ( T ) = y + COS( T )
for y( 0 ) = 0 given that y( 0 ) = 0

1 - write the Differential Equation in the field f
2-Access Solve Application:

HP49 Red Shift [NUM SLV] if you are using HP49.
HP48 Right Shift [SOLVER] if you are using HP48.

and choose 2-Solve dif eq..
Access Dif Eq Solver
3 - write the Differential Equation
in the field f
Writting the Dif Eq
4 - enter independent
and dependent variables,
the limits and press [SOLVE]
Solving the Dif Eq
Press [ENTER]
to see the result in the stack
Result in the stack

What are the variables enclosed?
Variables enclosed are to, t and yo
Given a differential equation y'( T ) = y + COS( T )
to solve it for y( T ) given that y ( to ) = yo
the variables can be written
as in the picture beside.
Symbolic example

Solve the Differential Equation
y'( T ) = y + COS( T )
for y( 3 ) given that y ( 1 ) = 2

Numeric example