73.8.18 problem 13.3 (c)

Internal problem ID [15226]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.3 (c)
Date solved : Tuesday, January 28, 2025 at 07:50:24 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 }&=2 \sqrt {y^{\prime \prime }} \end{align*}

✓ Solution by Maple

Time used: 0.255 (sec). Leaf size: 36

dsolve(diff(y(x),x$3)=2*sqrt(diff(y(x),x$2)),y(x), singsol=all)
 

\begin{align*} y &= c_{1} x +c_{2} \\ y &= \frac {1}{12} x^{4}+\frac {1}{3} c_{1} x^{3}+\frac {1}{2} c_{1}^{2} x^{2}+c_{2} x +c_{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 39

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

\[ y(x)\to \frac {x^4}{12}+\frac {c_1 x^3}{6}+\frac {c_1{}^2 x^2}{8}+c_3 x+c_2 \]