Give the correct answer and solve the given equation displaystylefrac{{left.{d}{y}right.}}{{left.{d}{x}right.}}=frac{{{y}^{2}-{1}}}{{{x}^{2}-{1}}},{y}{left({2}right)}={2}

Bevan Mcdonald 2020-11-02 Answered
Give the correct answer and solve the given equation dydx=y21x21,y(2)=2
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Expert Answer

Lacey-May Snyder
Answered 2020-11-03 Author has 88 answers
Given that
dydx=y21x21,
y(2)=2
dydx=y21x21
dyy21=dxx21
dyy21=dxx21
ln(|y1|)|y+1|=ln(|x1|)|x+1|+lnc.
Now putting y(2)=2 we have
ln13=ln13+lnc
13=c13
c=1
Therefore we have
ln(|y1|)y+1=ln(|x1|)|x+1|+ln1
ln(|y1|)y+1=ln(|x1|)|x+1|
|y1|y+1=|x1||x+1|
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