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

1 Answer
Apr 14, 2018

See below.

Explanation:

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.