Internal problem ID [15209]
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: 351.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(y(x)*diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y &= 0 \\ y &= {\mathrm e}^{c_{1} x} c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 14
DSolve[y[x]*y''[x]==y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{c_1 x} \]