Mat1512 assignment 5 2023

MAT1512
ASSIGNMENT 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.