Solve differential equation xy'+[(2x+1)/(x+1)]y= x-1

Nannie Mack 2020-12-29 Answered
Solve differential equationxy+[(2x+1)/(x+1)]y=x1
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Gennenzip
Answered 2020-12-30 Author has 96 answers

xdy/dx+((2x+1)/(x+1))y=x1
Dividing whole equation by x
dy/dx+((2x+1)/(x+1))y=1/x(x1)
dy/dx+((2x+1)/(x+1))y=11/x
dy/dx+Py+Q
P=(2x+1)/(x2+x), Q=11/x
I.F.=ePdx=e(2x+1)/(x2+x)dx
Let x2+x=t then (2x+1)dx=dt
I.F.=ePdx=e(2x+1)/(x2+x)dx=e1/tdt=elogt=t=x2+x
Then solution is y I.F.=Q(I.F.)dx+c
y(x2+x)=(11/x)(x2+x)dx+c
y(x2+x)=(x2+xx1)dx+c
y(x2+x)=(x21)dx+c
y(x2+x)=x3/xx+c
Multilpying by 3
3y(x2+x)=x33x+3c
3y(x2+x)=x33x+3c (where c=3c)

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Jeffrey Jordon
Answered 2021-12-25 Author has 2087 answers

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