77.1.83 problem 109 (page 162)

Internal problem ID [17973]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 109 (page 162)
Date solved : Tuesday, January 28, 2025 at 11:19:09 AM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

\begin{align*} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \end{align*}

✓ Solution by Maple

Time used: 2.017 (sec). Leaf size: 39

dsolve(diff(y(x),x$3)= sqrt(1+diff(y(x),x$2)^2),y(x), singsol=all)
 

\begin{align*} y &= -\frac {1}{2} i x^{2}+c_{1} x +c_{2} \\ y &= \frac {1}{2} i x^{2}+c_{1} x +c_{2} \\ y &= \sinh \left (x +c_{1} \right )+c_{2} x +c_{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.251 (sec). Leaf size: 17

DSolve[D[y[x],{x,3}]== Sqrt[1+D[y[x],{x,2}]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 x+\sinh (x+c_1)+c_2 \]