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

If f(x)=f(x)+f′′(x)+f′′′(x)+...... and f(0)=1, then f(x)=

A
ex2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
ex
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
e2x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
e4x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A ex2
We have, f(x)=f(x)+f′′(x)+f′′′(x)+......(1)
Differentiate both sides,
f(x)=f′′(x)+f′′′(x)+...............(2)
Now subtract (2) from (1)
f(x)f(x)=f(x)
f(x)=2f(x)
f(x)f(x)=12
Now integrate both sides,
lnf(x)=12x+C
f(x)=Aex2
Now since f(0)=1A=1
Hence f(x)=ex2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Combinations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon