73.8.7 problem 13.2 (a)

Internal problem ID [15215]
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 : 13.2 (a)
Date solved : Tuesday, January 28, 2025 at 07:50:09 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \end{align*}

Solution by Maple

Time used: 0.678 (sec). Leaf size: 51

dsolve(diff(y(x),x$2)=4*x*sqrt(diff(y(x),x)),y(x), singsol=all)
 
\begin{align*} y &= c_{1} \\ y &= \frac {x^{5}}{5}-\frac {2 x^{3}}{3 c_{1}}+\frac {x}{c_{1}^{2}}+c_{2} \\ y &= \frac {x^{5}}{5}+\frac {2 x^{3}}{3 c_{1}}+\frac {x}{c_{1}^{2}}+c_{2} \\ \end{align*}

Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]==4*x*Sqrt[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {x^5}{5}+\frac {c_1 x^3}{3}+\frac {c_1{}^2 x}{4}+c_2 \]