SOLUTION: Please help me with this problem: Find a general solution to the differential equation {{{dy/dx}}} = {{{-x^2y^3}}}

Algebra ->  Test -> SOLUTION: Please help me with this problem: Find a general solution to the differential equation {{{dy/dx}}} = {{{-x^2y^3}}}      Log On


   

Question 1032007: Please help me with this problem:
Find a general solution to the differential equation dy%2Fdx = -x%5E2y%5E3
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y'=-x^2*y^3
separate the variables
y^(-3) dy/dx=-x^2
y^-3 dy =-x^2 dx
integrate both sides
-(1/2)y^(-2)=(-1/3)x^3; multiply both sides by -6.
(3/y^2)=2x^3; cross multiply
2y^2=(3/x^3)
y^2=(3/2x^3)
y=+/-sqrt(3/2)(1/x*sqrt(x))=[(3sqrt(2))/2]*1/[x*sqrt(x)]