60.1.518 problem 521

Internal problem ID [10532]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 521
Date solved : Monday, January 27, 2025 at 08:52:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 54

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

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