Differential Equations MAP 2301 Sanchez
Exam 2
Name: ______
I. Complete:
3. The general solution of the linear differential equation with constant coefficients and characteristic4. The linear differential equation with constant coefficients and characteristic roots -1, -1 and 0,
Solution:
5. The general solution of the homogeneous equidimensional –Euler Cauchy DE with characteristic
roots -1, -1 and 0 is: ______
6. If the characteristic roots of the associated homogeneous differential equation with constant
coefficients are 2-3i, 2+3i, and a particular solution of the non-homogeneous differential equation is
y=secx, then the general solution is
______
Work:
10. Write the general solution of the Linear Homogeneous Differential Equation with constant coefficients.
if the characteristic equation has the following roots: 0, 0, 3, 1+2i, 1-2i
answer:
Answer: __no solution______
answer: ______
answer: ______
20. Fill in the parenthesis uing the exponential shifting properties
______
a) Convert to a Cauchy-Euler D.E. by multiplication by x
b) The characteristic equation for the D.E. is ______where
c) The change of variable will transform the given differential equation to the following differential equation with constant coefficients:
d) The homogenous solution of the D.E. as a function of t is:
e) Using the variation of parameter technique, a particular solution as a function of t is given by
______where are functions of t
f) Write the system of equations necessary to find the functions
g) Using Cramer’s rule express each of the following in determinant form (do not solve)h) The solution of the differential equation as a function of t is
i) The solution of the differential equation as a function of x is
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