i" x? if
2 5 5; ? = my wa 2
G§§z§ff§§$ Q??? gw'ka féé/ W *5/55; Va w/
w
the general solutions of the following differential equations:
a) 5 i ) gmyx-l)
da: 3(4 ~ 3;)
Answer: QA//-w xix-v/ZthY/fc
2 3 2
b) _ (sec2m+3:52tanyw;y3) dx+ (x3
4
Name:
Section No.
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Number) on the course w eb p age, check here:
1 10.302 Differential Equations
Final Exam
May 5 , 2000
O ne sheet ( 2 sides, 8 ; X 11) of notes may be
MATH 315 FALL 1998 TEST 1 SOLUTION KEY
1. (15 pts.) Solve the differential equation
, with
.
Answer:
.
This is linear so find the integrating factor
Then
, so
.
Therefore
. Using
, we have
, so
and
, with
2. (15 pts.) Solve the differential equation
.
Ans
MATH 315 FALL 1998 TEST 2 SOLUTION KEY
1.
(15 pts.) Consider the differential equation y' +2y' + y = 0.
(a)
Find the general solution for the equation.
Answer:
Characteristic polynomial is r2+2r+1 = (r+1)2, with roots -1, -1.
The general solution is there
MATH 315 FALL 2006 TEST 2 KEY
1. (20 pts.) Consider the differential equation
1. Find the general solution for the equation.
Answer: characteristic polynomial is
.
, with roots 0, -1, 2.
The general solution is therefore
2. Determine the Wronskian for you
MATH 315 FALL 1998 TEST 3 SOLUTION KEY
1. (10 pts.) Use Power series to solve the differential equation y' + y = 3x ,
with y(0) = 1.
(a)
Find the recursion formula for the coefficients an in the power series
representation of the solution
.
Answer:
, so
S
MATH 315 FALL 2006 TEST 3 SOLUTION KEY
Note: the following solutions are for one version of the test; some final solutions for the
alternate test version problems are also given.
1. (20 pts.) Use Power series to solve the differential equation
with
1.
.
F