Internal problem ID [9277]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1699 (book 6.108).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime \prime } y+y^{2}-x a -b=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)*y(x)+y(x)^2-a*x-b=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 63
DSolve[-b - a*x + y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\frac {a x^3}{3}+b x^2+c_2 x+2 c_1} \\ y(x)\to \sqrt {\frac {a x^3}{3}+b x^2+c_2 x+2 c_1} \\ \end{align*}