Question #a8319

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Answer 1 · 2018-02-06T16:43:35

#5x^2-y^2=1#

#xy(dy)/(dx)-y^2=1#

rearrange as follows

#xy(dy)/(dx)=1+y^2#

#x(dy)/(dx)=(1+y^2)/y#

we have a first order separable variables

#int(y/(1+y^2))dy=intdx/x#

integrating writing the constant as#" "k#

#=>1/2ln|k(1+y^2)|=ln|x|" "------(GS)#

#boundary conditions

#x=1, y=2#

#1/2lnk5=ln1=0#

#:. ln5k=0=>k=1/5#

#:1/2ln(1/5(1+y^2))=lnx#

#ln(1/5(1+y^2))=2lnx=lnx^2#

#=>1/5(1+y^2)=x^2#

#5x^2-y^2=1#