60.7.117 problem 1708 (book 6.117)

Internal problem ID [11706]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1708 (book 6.117)
Date solved : Monday, January 27, 2025 at 11:30:27 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.080 (sec). Leaf size: 33

dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+a*y(x)*diff(y(x),x)+y(x)^2*b=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\frac {{\mathrm e}^{-a x} c_{1} a +\left (-b x -c_{2} \right ) a +b}{a^{2}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.249 (sec). Leaf size: 28

DSolve[b*y[x]^2 + a*y[x]*D[y[x],x] - D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 e^{-\frac {b x+c_1 e^{-a x}}{a}} \]