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MAT1512 ASSIGNMENT 5 2023
- Institution
- University Of South Africa (Unisa)
This document contains MAT1512 ASSIGNMENT 5 2023 solutions. Clear step by step calculations are provided.
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MAT1512ASSIGNMENT 5
2023
, QUESTION 1
Solution:
a).
dy
x2 + 4 − y3 =0
dx
dy
x2 + 4 = y3
dx
dy
y3 = x2 + 4
dx
y 3 dy = (x 2 + 4)dx
The differential equation is separable.
b).
dy √4 − y cos(√x)
=
dx y 2 √x
dy
y 2 √x = √4 − y cos(√x)
dx
, y2dy cos(√x)
=
√4 − y dx √x
y2 cos(√x)
dy = dx
√4 − y √x
The differential equation is separable.
c).
dy x+4
= 3
dx x csc(2y) cot(2y)
dy x + 4
csc(2y) cot(2y) = 3
dx x
x+4
csc(2y) cot(2y) dy = ( ) dx
x3
The differential equation is separable.
d).
dy 5x 2 y 2 + y 2
=
dx x 2 y 5 + 4x 2
dy (5x 2 + 1)y 2
= 2 5
dx x (y + 4)
y 5 + 4 dy 5x 2 + 1
( ) = ( )
y2 dx x2
y5 + 4 5x 2 + 1
( ) dy = ( ) dx
y2 x2
The differential equation is separable.
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