APM1514
ASSIGNMENT 3
2023
, QUESTION 1
Solution:
1.1).
dy 1
= (t 2 + 1)ey−t ( )
dt cos(y)
dy (t 2 + 1)ey
=
dt cos(y)et
cos(y) (t 2 + 1)
dy = dt
ey et
The differential equation is separable
1.2).
dy
2x 2 = x2 + y2
dx
dy x 2 + y 2
=
dx 2x 2
dy 1 y2
= (1 + 2 )
dx 2 x
dy 1 y 2
= (1 + ( ) )
dx 2 x
The differential equation is not separable and not solvable since x divides y.
ASSIGNMENT 3
2023
, QUESTION 1
Solution:
1.1).
dy 1
= (t 2 + 1)ey−t ( )
dt cos(y)
dy (t 2 + 1)ey
=
dt cos(y)et
cos(y) (t 2 + 1)
dy = dt
ey et
The differential equation is separable
1.2).
dy
2x 2 = x2 + y2
dx
dy x 2 + y 2
=
dx 2x 2
dy 1 y2
= (1 + 2 )
dx 2 x
dy 1 y 2
= (1 + ( ) )
dx 2 x
The differential equation is not separable and not solvable since x divides y.
