CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the curve y=y(x) satisfies the differential equation dydx2xy1+x2=0 and y(0)=1, then y(1) is equal to

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 2
dydx2xy1+x2=0
dyy=2xdx1+x2dyy=2xdx1+x2

Let I=2xdx1+x2
Assuming 1+x2=t2xdx=dt
I=dttI=ln|t|=ln|1+x2|
Hence, the general solution is ln|y|=ln|1+x2|+ln|C|
y=C(1+x2)
Putting x=0,y=1, we get
C=1
So, the required curve is,
y=1+x2
y(1)=2

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