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

If the solution of differential equation x ln xdydx+y=2lnx is y(lnx)=(lnx)n+C then n = ___

Open in App
Solution

Type of the differential equation is what you have to identify. Here if you divide the given equation by x lnx, it becomes dydx+1xlnx×y=2x which when compared to standard form of linear differential equation matches it. Here P(x) = 1xlnx
Q(x)=2x
Solution will be y X I.F = Q(I.F.)dx + C
I.F. = eP(x)dx
So I.F = lnx.
So general solution will be
y×lnx=2xlnxdx+C
ylnx=(lnx)2+C
So n = 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