29.37.12 problem 1130

Internal problem ID [5670]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1130
Date solved : Monday, January 27, 2025 at 01:04:32 PM
CAS classification : [_Clairaut]

\begin{align*} a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.694 (sec). Leaf size: 17

dsolve(a*(1+diff(y(x),x)^3)^(1/3)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = a \left (c_{1}^{3}+1\right )^{{1}/{3}}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 27

DSolve[a*(1+ (D[y[x],x])^3)^(1/3) +x D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to a \sqrt [3]{1+c_1{}^3}+c_1 x \\ y(x)\to a \\ \end{align*}