MAT3700 EXAM PACK 2026

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MAT3700
EXAM PACK


DISTINCTION QUALITY




UNISA EXAM

, MAT3700 2025


Solve the following first-order differential equations:


QUESTION 1: x  y  3 dy  4ydx (4)

ANSWER: x  y  3 dy  4ydx
y 3 4
dy  dx
y x
 3   4 
 1  y  dy    x  dx
   
y  3 ln y  4 ln x  C


 
QUESTION 2: x 3  y 3 dx  3 xy 2dy  0 [Hint: Put y  vx ] (7)

ANSWER:

x 3

 y 3 dx  3 xy 2dy  0
dy dv
Put y = vx then v x
dx dx
x 3

 v 3 x 3 dx  3 x 3v 2dy  0
dy x3  v 3x3

dx 3 x 3v 2
dv 1 v 3
vx 
dx 3v 2
2
 3v

dx
 dv 
 1  2v 3  x
1
 ln 1  2v 3  ln x  C
2
3
1 y
 ln 1  2    ln x  C
2 x




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