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Material Type: Assignment; Class: Calculus II; Subject: Mathematics; University: Illinois Institute of Technology; Term: Unknown 1989;
Typology: Assignments
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dx dt
= 2 x y
dy dt
= x
x = c (^) 1 e
t
t
dx dt
= y + t
dy dt
= x t
x = c (^) 1 cos + c 2 sin + t + y = c (^) 1 sin c 2 cos + t
1 Solve the given system of differential equations by systematic elimination.
Complete the answer.
2 Solve the given system of differential equations by systematic elimination.
Complete the answer.
2
x = c (^) 1 e t
^ t 3 cos 5 2
t + c (^) 3 e
^ t 3 sin 5 2
t
y = ^3 2
c 2 ^5 2
c (^) 3 e
^ t 2 cos 5 2
t + ^5 2
c (^) 3 ^5 2
c 2 e
^ t 3 sin 5 2
t
x = c (^) 1 e t
^ t 2 cos 3 2
t + c (^) 3 e
^ t 2 sin 3 2
t
y = ^3 2
c 2 ^3 2
c (^) 3 e
^ t 2 cos 3 2
t + ^3 2
c (^) 3 + 3 2
c 2 e
^ t 2 sin 3 2
t
x = c (^) 1 e
t
^ t 2 cos 5 2
t + c (^) 3 e
^ t 5 sin 5 2
t
y = ^5 2
c 2 ^5 2
c (^) 3 e
^ t 5 cos 3 5
t + ^3 5
c (^) 3 ^3 5
c 2 e
^ t 5 sin 3 5
t
x = c (^) 1 e t
^ t 2 cos 7 2
t + c (^) 3 e
^ t 2 sin 7 2
t
y = ^7 2
c 2 ^7 2
c (^) 3 e
^ t 2 cos 7 2
t + ^7 2
c (^) 3 ^7 2
c 2 e
^ t 2 sin 7 2
t
x = c (^) 1 e
t
^ t 2 cos 3 2
t + c (^) 3 e
^ t 2 sin 3 2
t
y = 3 2
c 2 + 3 2
c (^) 3 e
^ t 2 cos 3 2
t + ^3 2
c (^) 3 + 3 2
c 2 e
^ t 2 sin 3 2
t
3 Solve the given system of differential equations by systematic elimination.
a.
b.
c.
d.
e.
1. t; t^1 t; t 2.
t; t;
t; t;
3. b 4. t; t;; t ; 5. c
ANSWER KEY Page 1
ANSWER KEY
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