Internal problem ID [13170]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 36
dsolve(diff(y(x),x$3)=2*sqrt(diff(y(x),x$2)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x +c_{2} y \left (x \right ) = \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: 0.13 (sec). Leaf size: 39
DSolve[y'''[x]==2*Sqrt[y''[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{12}+\frac {c_1 x^3}{6}+\frac {c_1{}^2 x^2}{8}+c_3 x+c_2 \]