wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Which of the following functions are not homogeneous?

A
x+ycosyx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
xyx+y2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
xycosxysinx+y
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
xyln(yx)+yxln(xy)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct options are
B xyx+y2
C xycosxysinx+y
Consider f(x) to be homogeneous.
Then it should satisfy the condition, f(vx)=vf(x) or in other words, replacing x by (vx) and y by (vy) should give us v times the same initial expression, where v is an arbitrary constant.
For example consider option A
Replacing x by (vx) and y by (vy)
vx+vycos(vyvx)
=v(x+ycos(yx))
The degree of all the terms is same.
However these conditions are not met by B and C.
Hence Options B and C are non-homogenous.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Methods of Solving First Order, First Degree Differential Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon