Solve the differential equationx dy/dx-y= x^2lnx

Reeves 2020-11-16 Answered

Solve the differential equation xdy/dxy=x2lnx

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Expert Answer

Alix Ortiz
Answered 2020-11-17 Author has 109 answers

Divide both sides by x and further simplify it
x/xdy/dxy/x=(x2lnx)/x
dy/dxy/x=xlnx
It is of the form dy/dx+P(x)y=Q(x)
Now find the integrating factor by using (I.F.)=eP(x)dx
Hence, I.F.=e1/xdx
=elnx
=eln1/x
=1/x
Hence, I.F.=1/x
y(I.F.)=(I.F.)Q(x)dx+c
Hence, y1/x=1/xxlnxdx+c
y1/x=lnxdx+c
y1/x=lnx1dx+c
y1/x=lnx+x+c
Simplify
y1/x=x(lnx+1)+c
y=x2(lnx+1)+cx

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