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PROBLEM SET 4
1. Indicate if the equation is exact or not.
If it is exact, find the solution.
a)
e
y
d
x + (xe
y
– siny)
d
y = 0
b)
(9x
2
+ y –1)
d
x – (4y – x)
d
y = 0 ,
y(1)=0
c)
(x + y)
d
x – x
d
y = 0
d)
y’ =
g
G
– ±²g
³g´µ²
¶
·µ²g
¶
e)
d
x + (x/y – siny)
d
y = 0
For problems 2 through 4, find the general solution of the differential equation.
2.
y” + 4y’ + 4y = 0
3.
y” – 5y = 0
4.
y”  y’ – 2y = 0
For problems 5 through 7, find the solution to the initial value problem.
5.
6y” – 5y’ + y = 0
y(0) = 4,
y’(0) = 0
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Unformatted text preview: 6. y” + 8y’ – 9y = 0 y(1) = 1 y’(1) = 0 7. 4y”y=0 y(2)=1 y’(2)=1 8. Find a differential equation whose general solution is y = c 1 e 2t + c 2 e3t 9. Find the solution of the initial value problem 2y”3y’+y=0, y(0)=2, y’(0)=1/2. Then determine the maximum value of the solution and also find the point where the solution is zero. 10. Solve the initial value problem y”y’2y=0, y(0) = a, y’(0) = 2. Then find “a” so that the solution approaches zero as t b ∞...
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This note was uploaded on 12/08/2011 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Fonken

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