Equate the function and its derivatives to the initial
conditions and place them in a vector named z(x).
Now, we use the initial conditions to form the linear
system in for the unknowns c1, c2 ,c3.
Define the general solution
c) To find a particular solution, we first form the
The Wronskian is never zero since e
3x is never zero. Thus, the solutions are linearly
The above results can be simplified using the simplify
b) To show that the three solutions are linearly independent,
we first define the Wronskian of the solutions
then compute it
This way you take care of the definition of y1(x) wither
the root is real or complex. Similar definitions can
be given to the other solutions.
Left-hand side is zero which is equal to the right-hand
We can verify our solution by substituting y(x) and
its derivatives in the diff. eqn
Display the particular soln.
You must redefine the general solution again.
Use the values returned in s to define the constants
c1, c2 and c3.
The particular solution is given by
Use the solve command to find c1, c2 and c3. Name the
Evaluate the function and its derivatives ant x = 0.
We can display the roots using the subscripts of r as
Use Mathcad solve
command to find the roots of the char. poly and name
the solution r. Mathcad will return the roots in a
3 x 1 vector.
Define the characteristic poly.
Force Mathcad to start the subscription from 1 rather
The solution of this quiz will illustrate how to use
Mathcad to answer the above questions
Given the differential equation y'' - 3y'' + 25y' +
29y = 0,
a) find three linearly independent solutions to the
b) show that the three solutions are linearly independent.
Justify your answer.
c) find a particular solution satisfying the initial
y(0) = 20, y'(0) = -40,
and y''(0) = 110
This worksheet should be used as guide for solving the
You can make your definitions of the solution more general
by creating the definitions in the following manner
Use the above roots to construct the three solutions:
The commands Re and Im are used to refer to the real
and imaginary parts of a complex number. In our example,