75.14.19 problem 345

Internal problem ID [16933]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 345
Date solved : Tuesday, January 28, 2025 at 09:41:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=\sqrt {1+y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.659 (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: 0.067 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]==Sqrt[1+D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} x \left (x^2+3 c_1 x+3 \left (-4+c_1{}^2\right )\right )+c_2 \]