x(logx) dy/dx + y =2(logx).......plz help me to how to solve it???????

dy/dx + y/xlogx = 2/x

we have i.f = eintegral 1/xlog x

put x= et

on solving we get I.F= logx

now solve by formula, y. I.F = integral 2/x I.F dx

you will get answer = ylogx = (logx)2

  • -15
Xlogx dy/dx+y 2/x logx Dividing by Xlogx --- Dy/dx + (1/Xlogx)y=2/x^2 Comparing with dy/dx+py=Q---- P=1/(Xlogx), Q=2/x^2 Now IF= e^[int(1/Xlogx)dx Let logx=u du=1/x dx xdu=dx So IF=e^[int{(1/xu).xdu}] IF=e^[int(1/u)du] IF=e^logu=solution of the equation Y×IF=[int(Q×IF)dx]+c ylogx=[int(2/x^2 × logx)dx]+c Let I = 2[int(logx × x^-2)dx]+c or, I=2[-logx/x+ int1/x^2dx] or, I=2[lox/x+ x^-1/(-1)] or, I = -2/x(1+logx) Putting value of I in the equation ylogx=-2/x(1+logx)+c
  • -7
Hello hi madam
  • 0
Complete

  • -2
What are you looking for?