The University of Sydney
School of Mathematics and Statistics
PRACTICE Quiz 2
MATH2021 Vector Calculus and Differential Equations Semester 1, 2023
The actual quiz will have 10 Multiple Choice questions
1. Which of the following differential equations are linear?
(Do not solve the equations.)
(A) x2
dy
dx
= x + 6x3y, (B) x
dx
dt
= 4
x
t2
+ t3x2,
(C) sin(t)
dx
dt
= 5 + xex, (D) y
dy
dx
= 3 sin(x) + 6y + x2.
2. Calculate the particular solution of the differential equation
y′′ + 7y′ + 12y = 0, y(0) = 1, y′(0) = 2,
3. Calculate the general solution of the differential equation
dy
dx
= x− 4
x
y.
4. Calculate the general solution of the differential equation
1
x2
dy
dx
+ 7x4y2 = 0.
5. Calculate the general solution of the differential equation
(x2 − 3x)dy
dx
= y.
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6. Calculate the general solution of the differential equation
y′′ − 6y′ + 25y = 0.
7. Use the table of Laplace transforms to calculate the transform of the function
f(t) = e−3t cosh 4t.
8. Use the table of Laplace transforms to calculate the inverse transform
of the function: F (s) =
12
s4
9. Calculate the particular solution yp(x) of the differential equation
y′′ + 4y = x2 + x + 1.
10. Which of the following differential equations are separable?
(Do not solve the equations.)
(A)
dy
dx
= 2xy + 5 + 10x + y, (B) x2
dy
dx
= 1 + x + yx,
(C) x
dy
dx
=
2x + y2
x
− 2, (D) e−x dy
dx
= 3 + y2 tanx.
2