Find the general solution of #dy/dx = (1+x)/(x-1)# ?

Question

x=2, y=1

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Answer 1 · 2018-06-10T12:42:24

#y=x-1+2Ln(x-1)#

#dy/dx=(x+1)/(x-1)#

#dy=(x+1)/(x*1)*dx#

#y=int ((x+1)*dx)/(x-1)#

=#int ((x-1)*dx)/(x-1)+int (2*dx)/(x-1)#

=#int dx+int (2*dx)/(x-1)#

=#x+2Ln(x-1)+C#

After plugging #x=2# and #y=1# into equation,

#2+2Ln1+C=1# or #2+C=1#, thus #C=-1#

Thus, #y=x-1+2Ln(x-1)#