Internal problem ID [15216]
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: 358.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {2 y y^{\prime \prime }-{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(2*y(x)*diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
\[ y = \frac {\left (c_{1}^{2}+1\right ) x^{2}}{4 c_{2}}+c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[2*y[x]*y''[x]==1+y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (1+c_1{}^2\right ) x^2}{4 c_2}+c_1 x+c_2 \\ y(x)\to \text {Indeterminate} \\ \end{align*}