Matching Game ­ Separated ODE's
Robert Maˇr´ik
Instructions: Select a question clicking its checkbox. Solve the problem and find the
answer. No guessing! A maximum of 3 tries on any problem before you get 3 penalty
points ! Passing is to complete the puzzle with only 4 incorrect answers.
To the picture: He was born on May 10, 1899 in Uhersk´y
Ostroh and died on July 22, 1995 in Brno. He was a Czech
mathematician best known today for his work in graph theory
and in theory of differential equations, namely he established
theory of global transformations of second order differential
equations.
Who is he? ­ Solve problems on next page.
Questions
1. y =
y2
+ 1
x2 + 1
2. y =
x
y
3. y =
ex
ey
4. y =
y
y2 + 1
x
5. y = ex
ey
6. y =
x2
+ 1
y2 + 1
7. y =
y2
+ 1
y
x
8. y =
1
y
9. y = cos2
y cos x
Answers
a. ln(y2
+ 1) = x2
+ C
b. y2
= x2
+ C
c. tg y = sin x + C
d. y2
+ y = x2
+ C
e. arctg y = arctg x + C
f. y = ln(C - ex
)
g. y = ln(ex
+ C)
h. y = - ln(C - ex
)
i. y2
= 2x + C
j. y3
+3y = 3 arctg x+C
k. y3
+ 3y = x3
+ 3x + C
l. y2
+ ln(y2
) = x2
+ C