MATH 450
HOMEWORK 6
SOLUTION OF DIFFERENTIAL EQUATIONS USING
POWER SERIES METHOD
Question 1
Apply power series method to obtain the solution
of y+xy=0. Compare this with the result obtained
using MATLAB desolve function.
Solution:
.y= a0 +a1 x +a2 x2 + a
MATH 450 HOMEWORK 4
NUMERICAL METHOS OF SOLVING DIFFERENTIAL
EQUATIONS
1. Find an ODE for which the given functions e2x,
x e2x, and x2e2x form a basis of solutions. Verify
the result using MATLAB.
Solution:
Roots of The D Equation
Da =0
D= a
Example
MATH 450
HOMEWORK 5

This chapter can be summarized in following steps.
Change of variables can convert a second order
differential equation to system equations.
Example
.y 10y +24y =0
y(1) = 2, y(1)=3
Let x1(t)= y(t)
.x2(t)= y (t)
Differentiate both e
MATH 450 Homework 3
The equation y1= x3 and y2= x5 form the basis of 2nd
order ODE x2 y 7x y 15y =0. Solve the initial value
problem for the ODE given y(1) =0.4 and y(1)= 1. (A)
Solution:
Let the solution is
.y(x)= Ax3 +B x5
.y(1) = A +B = 0.4 (1)
Now
Homework 1
1. Given Z1=2+3i , Find Z1*/Z1
Solution
Z1* = compliment of z1= 23i
23 i
2+ 3i
Rationalize the denominator (get rid of i term) by
multiplying the numerator and denominator by
conjugate of 2+3i which is 23i
23 i
2+ 3i
*
23 i
23 i
=
46 i6 i+9 i
HOMEWORK 2
1.
Which one of the following is the solution of
the ordinary DE y= e3x (B)
Solution
.y = e3x
dy
3x
dx = e
dy = e3x dx
Integrate both sides
dy = e dx
y = e3 + C
Where C is constant of integration
2. Verify that cex +x +1 is the solution o
DeVry University
MATH45014300 Advanced Engineering Mathematics I
Home Work #2
Professor: Randall Sharpe
Student Name:
1.
(TCO 1) which of the following functions is the solution to the given ODE
'
3 x
y =e
?
Type equation here .
2.
(TCO 1) Verify that
y