Internal problem ID [15214]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 356.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-y^{\prime }-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(y(x)*diff(y(x),x$2)=diff(y(x),x)+diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y &= 0 \\ y &= \frac {{\mathrm e}^{c_{1} \left (x +c_{2} \right )}+1}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.452 (sec). Leaf size: 26
DSolve[y[x]*y''[x]==y'[x]+y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1+e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}