Math 301 Exam 1
Name:
Problem 1
Solve the separable ODE completely
Solution:
Problem 2
The ODE
is homogeneous (Do not waste time verifying it). Make
necessary substitutions to transform the ODE as a separable ODE. Do not solve the resulting
separable ODE.
Math 301 Exam 1 Practice Guide
Problem 1
Solve the separable ODE completely
Solution: Separate variables:
Integrate:
(1.1)
Substitute
:
(1.2)
(1.3)
(1.3)
Namely
and the final solution is
Problem 2
The ODE
is homogeneous (Do not waste time verifying it). M
Math 301 Exam 1 Practice Guide
Problem 1
Solve the separable ODE completely
2
y$dy C x$dx = 3$x$y $dx, y 2 = 1
Problem 2
2
3
2
3
Verify the ODE x$y K 2$x y 'C 2$x $y C y = 0 as homogeneous. Then make necessary
substitutions to transform the ODE as a separ
Math 301 Exam 1 Practice Guide
Problem 1
Solve the separable ODE completely
2
y$dy C x$dx = 3$x$y $dx, y 2 = 1
Solution:
We can separate the variables by manipulating the ODE as follows
2
y$dy = K $dx C 3$x$y $dx
x
2
y$dy = 3$x$y K x $dx
y$dy = 3$y2 K 1 $
Exam 2 practice problems
1. Solve
(Answer in 20131007.pdf, page 2)
2. Solve
(Answer in 20131009.pdf)
for its general real solutions.
3. Solve
,
by variation of parameters (Answer in 20131016)
4. Solve
pdf, page 3)
5. Solve
,
and
by Laplace transform. (Ans
Homework 02 Answer
Page 56, #13 y '= y$ln y $cot x
dy
= y$ln y $cot x .
dx
Multiplying both sides with dx yields dy = y$ln y $cot x $dx
dy
Separate x and y:
= cot x $dx
y$ln y
1
Integrate
dy = cot x dx C C; and obtain the 1-parameter family of solutions
y
Homework 03 Answer:
Page 61, #8
Solution: The ODE is in the form of
where
Since
(1.1)
(1.1)
that is
, and
(1.2)
that equals to
, both are homogeneous functions of order zero. Therefore
the ODE is homogeneous.
Make substitution
(1.3)
(1.4)
Namely
Integrate