MAT3700 Assignment 02 Answers 2025 – 15 Verified Questions with Correct Solutions | A+ Grade Guaranteed

1




MAT3700 Assignment 02 Answers
2025 – 15 Verified Questions with
Correct Solutions | A+ Grade
Guaranteed

Differential Equations (4 Questions)
Question 1

What is the general solution to a first-order linear differential equation of the form dy/dx + P(x)y
= Q(x)?
A) y = e^(-∫P(x)dx) [∫Q(x)e^(∫P(x)dx)dx + C]
B) y = Q(x)/P(x) + C
C) y = e^(∫P(x)dx) + C
D) y = ln|Q(x)| + C
Rationale: The general solution uses an integrating factor, e^(∫P(x)dx), per standard differential
equation techniques (Boyce & DiPrima, 2025).

Question 2

Which method is most appropriate for solving a homogeneous second -order differential equation
with constant coefficients?
A) Separation of variables
B) Characteristic equation method
C) Variation of parameters
D) Laplace transform
Rationale: The characteristic equation method efficiently solves homogeneous equations with
constant coefficients, per 2025 UNISA curriculum.

Question 3

For the differential equation d²y/dx² - 4y = 0, what is the general solution?
A) y = Ae^(2x) + Be^(-2x)
B) y = A cosh(2x) + B sinh(2x)
C) y = A sin(2x) + B cos(2x)
D) y = Ax + B
Rationale: The characteristic equation r² - 4 = 0 has roots ±2, leading to a hyperbolic solution,
per 2025 mathematical standards.