60.7.108 problem 1699 (book 6.108)

Internal problem ID [11697]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1699 (book 6.108)
Date solved : Monday, January 27, 2025 at 11:30:13 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime } y+y^{2}-a x -b&=0 \end{align*}

✗ 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: 0.523 (sec). Leaf size: 63

DSolve[-b - a*x + D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 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*}