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

The differential equation satisfied by the curves e2y+2bxey+b2=0, where b is a parameter, is

A
(1+x2)d2ydx2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(x21)(dydx)21=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(x21)d2ydx2+2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(x2x)dydxy2=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B (x21)(dydx)21=0
e2y+2bxey+b2=0
e2y+2bxey+b2x2=b2x2b2
(ey+bx)2=b2(x21)
ey+bx=±bx21
ey=b(x±x21) (1)

Differentiating equation (1) with respect to x, we get
eydydx=b(x21±x)x21 (2)

From equations (1) and (2),
x21dydx=±1
(x21)(dydx)2=1

flag
Suggest Corrections
thumbs-up
16
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Formation of Differential Equation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon