Math 20D SP22 Practice Midterm 1 Version A
50 minutes, Total points: 40
Name: PID:
Instructions:
1. Print your name and PID above, and print your name on the top of EACH page.
2. Except for problem 0, show all your works in the space provided. No credit will be given for unsupported
answers, even if correct.
3. No calculators, tablets, phones, or other electronic devices are allowed during this exam. You may use
one sheet of handwritten notes(double sided), but no books or other assistance.
4. The last page is your scratch paper and will not be considered, unless you specify in your work that part
of your answer is written on the last page. More scratch paper will be provided during the exam.
0. (1 point) Follow the instructions on above and any additional instructions given during the
exam.
1. (9 points) For the following ordinary differential equations, give the order, indicate the indepen-
dent and dependent variables, and indicate whether the equation is linear or non-linear.
(i) (3 points) √
1 y d
2y
dx2
+ 2x
dy
dx
= 0
(ii) (3 points)
d(t3)
dt
d3N
dt3
1
t
dN
dt
+ tN + t2 = 0
(iii) (3 points) (dy
dx
+ y
)2
+
d2y
dx2
x2 = 0
1
Name:
2. (10 points) Find the general solution to the differential equation
dy
dx
=
y
x
+ x2 sin(x)
2
Name:
3. (10 points) Find the general solution to the following differential equation
dy
dx
=
y2 + 2xy
x2
Hint: It may be a good idea to rewrite this as an equation involving a differential form.
3
Name:
4. (10 points) Solve the following initial value problem
y′′ 6y′ + 9y = 0, y(0) = 2, y′(0) = 9.
4
Scratch paper
5
Scratch paper
6
