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

The differential equation representing the family of curves y=xecx, where c is a constant, is


A
dydx=yx(1lnyx)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
dydx=yxln(yx)+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
dydx=yx(1+lnyx)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
dydx+1=yxlnyx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C dydx=yx(1+lnyx)
y=xecx
yx=ecx
Taking ln both sides, we get
lnyx=lnecx
lnyx=cx
1xlnyx=c
Differentiating both sides w.r.t. x :
1x(xy×1x2(xdydxy))+lnyx(1x2)=0
1xy(dydx)=1x2(lnyx+1)
dydx=yx(lnyx+1)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon