Internal problem ID [4326]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1130.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_Clairaut]
\[ \boxed {a \left (1+{y^{\prime }}^{3}\right )^{\frac {1}{3}}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.547 (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)
\[ y \left (x \right ) = a \left (c_{1}^{3}+1\right )^{\frac {1}{3}}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 27
DSolve[a (1+ (y'[x])^3)^(1/3) +x y'[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*}