29.35.1 problem 1030

Internal problem ID [5599]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1030
Date solved : Monday, January 27, 2025 at 12:13:10 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 46

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

\begin{align*} y \left (x \right ) &= -\frac {2 \sqrt {3}\, \sqrt {-a x}\, x}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {3}\, \sqrt {-a x}\, x}{9} \\ y \left (x \right ) &= \frac {c_{1} \left (a x +c_{1}^{2}\right )}{a} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 68

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

\begin{align*} y(x)\to \frac {c_1{}^3}{a}+c_1 x \\ y(x)\to -\frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}} \\ \end{align*}