MAT3700
ASSIGNMENT 1 2026
DUE: 4 MAY 2026
, MAT3700 ASSIGNMENT 1 2026
DUE 4 MAY 2026
Solve the following first-order differential equations, question 1 to 4.
QUESTION 1
1. Solve the differential equation:
dy
cos(y) = 3x 2 sin(x 3 )
dx
QUESTION 1 (Separable ODE)
dy
cos y = 3x2 sin(x3 )
dx
Separate variables:
cos y dy = 3x2 sin(x3 ) dx
Integrate both sides:
∫ cos y dy = ∫ 3x2 sin(x3 ) dx
Left side: ∫ cos y dy = sin y + C1
Right side: Let u = x3 , then du = 3x2 dx
∫ 3x2 sin(x3 )dx = ∫ sin u du = − cos u + C2 = − cos(x3 ) + C2
Equating:
sin y = − cos(x3 ) + C
where C = C2 − C1 .
sin y + cos(x3 ) = C
ASSIGNMENT 1 2026
DUE: 4 MAY 2026
, MAT3700 ASSIGNMENT 1 2026
DUE 4 MAY 2026
Solve the following first-order differential equations, question 1 to 4.
QUESTION 1
1. Solve the differential equation:
dy
cos(y) = 3x 2 sin(x 3 )
dx
QUESTION 1 (Separable ODE)
dy
cos y = 3x2 sin(x3 )
dx
Separate variables:
cos y dy = 3x2 sin(x3 ) dx
Integrate both sides:
∫ cos y dy = ∫ 3x2 sin(x3 ) dx
Left side: ∫ cos y dy = sin y + C1
Right side: Let u = x3 , then du = 3x2 dx
∫ 3x2 sin(x3 )dx = ∫ sin u du = − cos u + C2 = − cos(x3 ) + C2
Equating:
sin y = − cos(x3 ) + C
where C = C2 − C1 .
sin y + cos(x3 ) = C
