wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

If y(x) is the solution of the differential equation dydx+(2x+1x)y=e2x, x>0, where y(1)=12e2, then:

A
y(x) is decreasing in (12,1)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
y(x) is decreasing in (0,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
y(loge 2)=loge28
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
y(loge 2)=loge24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C y(loge 2)=loge28
dydx+(2x+1x)y=e2x, x>0
IF=e(2xx+1x)dx=xe2x

y×xe2x=x dx
y×xe2x=x22+c
y(1)=12e2,
12e2×e2=12+cc=0
y=xe2x2
y(loge2)=(loge2)e2loge22=loge28
dydx=12e2x(2x+1)
y(x) is decreasing in (12,1)

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