Internal problem ID [15203]
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: 345.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-\sqrt {y^{\prime }+1}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)=sqrt(1+diff(y(x),x)),y(x), singsol=all)
\begin{align*} y &= -x +c_{1} \\ y &= \frac {1}{12} x^{3}+\frac {1}{4} c_{1} x^{2}+\frac {1}{4} c_{1}^{2} x -x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 30
DSolve[y''[x]==Sqrt[1+y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} x \left (x^2+3 c_1 x+3 \left (-4+c_1{}^2\right )\right )+c_2 \]