What is the solution to the differential equation dy/dx= x-y^2 ?

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Answer 1 · 2018-04-14T23:27:05

See below.

Making the substitution

#y =(u')/u# and substituting we get

#u''-xu =0#

This is a linear differential equation with solution not representable with elementary functions.

NOTE

A series solution can be worked-out so making

#u = sum_(k=0)^oo a_k x^k# we obtain the recurrence relationship

#(k+3)(k+2)a_(k+3) = a_k# with two basic sequences

#{(a_3 = a_0/(2 xx 3)),(a_4 = a_1/(3 xx 4)):}# etc.