MAT3700 Assignments 1 Due 2026

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


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MAT3700: Differential Equations

Assignment 1 — Year 2026

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MAT3700
Module Code:
Differential Equations
Module Name:
Solving First-Order Differential Equations
Assignment Topic:
Assignment Number 1
Assignment Number:
35
Total Marks:




Submitted in partial fulfilment of the requirements for [Module Name] — UNISA [Year]

, UNISA | MAT3700 Differential Equations Assignment



Question 1

Solve the differential equation:


dy
cos(y) = 3x2 sin(x3 )
dx

(3)


Solution


Step 1: Separate variables



cos(y) dy = 3x2 sin(x3 ) dx


Step 2: Integrate both sides

Left side:
Z
cos(y) dy = sin(y)


Right side – substitute u = x3 , du = 3x2 dx:

Z Z
3x2 sin(x3 ) dx = sin(u) du = − cos(u) = − cos(x3 )



Step 3: Combine



sin(y) = − cos(x3 ) + C




sin(y) + cos(x3 ) = C




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