UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
DIFFERENTIAL EQUATIONS
Mathematics Assignment
⋄
Module Code: MAT3700
Module Name: Differential Equations
Assignment No.: Assignment Number 1
Submitted in partial fulfilment of the requirements for Differential Equations
at the University of South Africa.
, UNISA | Differential Equations Mathematics Assignment
Question 1 [3]
Solve the differential equation:
dy
cos(y) = 3x2 sin(x3 )
dx
Solution
Step 1: Separate the variables.
cos(y) dy = 3x2 sin(x3 ) dx
Step 2: Integrate both sides.
Left side:
Z
cos(y) dy = sin(y)
Right side — let u = x3 , so du = 3x2 dx:
Z Z
3x2 sin(x3 ) dx = sin(u) du = − cos(u) = − cos(x3 )
Step 3: Combine results.
sin(y) = − cos(x3 ) + C
Final Answer
sin(y) + cos(x3 ) = C
Page 1 of 9
College of Science, Engineering and Technology
⋄
DIFFERENTIAL EQUATIONS
Mathematics Assignment
⋄
Module Code: MAT3700
Module Name: Differential Equations
Assignment No.: Assignment Number 1
Submitted in partial fulfilment of the requirements for Differential Equations
at the University of South Africa.
, UNISA | Differential Equations Mathematics Assignment
Question 1 [3]
Solve the differential equation:
dy
cos(y) = 3x2 sin(x3 )
dx
Solution
Step 1: Separate the variables.
cos(y) dy = 3x2 sin(x3 ) dx
Step 2: Integrate both sides.
Left side:
Z
cos(y) dy = sin(y)
Right side — let u = x3 , so du = 3x2 dx:
Z Z
3x2 sin(x3 ) dx = sin(u) du = − cos(u) = − cos(x3 )
Step 3: Combine results.
sin(y) = − cos(x3 ) + C
Final Answer
sin(y) + cos(x3 ) = C
Page 1 of 9
