Internal problem ID [3818]
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]
Solve \begin {gather*} \boxed {a \left (1+\left (y^{\prime }\right )^{3}\right )^{\frac {1}{3}}+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.302 (sec). Leaf size: 124
dsolve(a*(1+diff(y(x),x)^3)^(1/3)+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = a \left (c_{1}^{3}+1\right )^{\frac {1}{3}}+c_{1} x \\ y \relax (x ) = \left (x^{\frac {3}{2}} c_{1}+a^{3}-x^{3}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (x^{\frac {3}{2}} c_{1}+a^{3}-x^{3}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x^{\frac {3}{2}} c_{1}+a^{3}-x^{3}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (x^{\frac {3}{2}} c_{1}+a^{3}-x^{3}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x^{\frac {3}{2}} c_{1}+a^{3}-x^{3}\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.135 (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*}