What is a solution to the differential equation dy/dx= y^2? (Please)

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Answer 1 · 2018-04-17T22:54:37

#y(x)=-1/(x+C)#

This is a separable differential equation. We'll get all #y,dy# on the right side and all #x,dx # on the left.

#dy/dx=y^2#

#1/y^2dy=dx#

Note that we have no #x# so all we do is move #dx# to the left.

#y^-2dy=dx#

Integrate both sides:

#inty^-2dy=intdx#

#-1/y=x+C#

We need an explicit solution in the form #y(x):#

#-1=y(x+C)#

#y(x)=-1/(x+C)#

Answer 2 · 2018-04-17T23:16:58

#y=-1/(x+C)#

#(dy)/dx=y^2#
#y^(-2)dy=dx#
#inty^(-2)dy=intdx#
#-y^(-1)=x+C#
#y^(-1)=-x-C#
#y=1/(-x-C)#
#y=-1/(x+C)#, #C# is a constant