Solving Linear Ordinary Differential Equations
By including the below Mathcad sheet as a reference, it is possible to solve Linear Ordinary Differential Equations with constant coefficients.
Note that an include sheet exists for Mathcad 11 (LODEsolve.mcd) separately from Mathcad 15 (LODEsolve.xmcd). The Mathcad 11 sheet will not work in Mathcad 15. If you are using Mathcad 11, change the reference below accordingly.
The function
Examples:
For a differential equation as:
The solution is:
Proof:
The initial condition
Expressions on either side
of the
Use u(x) numerically, for plotting:
Note that
results in essentially the same function.
And also
Note that you
cannot:
since the coefficient of the first derivative is not a constant
For a differential equation
and
The solution is:
then:
Proof:
yes, it's 0