1.2 Algorithm pseudocode

1.2.1 Main solver (section 3-1 in Murphy)
1.2.2 First special case. The reduced Riccati solver (section 3-2 in Murphy book)
1.2.3 Second special case. (section 3-3 in Murphy book)
1.2.4 Transform to \(u'=F(x)+u^2\). remove linear term. section 3-1-3 in Murphy
1.2.5 Special solutions. section 3-1-2 in Murphy
1.2.6 Helper function. Used by Second special case
1.2.7 General solver. Converts to second order. Used if all above fail