1.520 problem 521

Internal problem ID [8101]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 521.
ODE order: 1.
ODE degree: 3.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+x y^{\prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.262 (sec). Leaf size: 19

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

\begin{align*} y \relax (x ) = c_{1}^{3}+c_{1} x \\ y \relax (x ) = x^{\frac {3}{2}} c_{1} \\ \end{align*}

Solution by Mathematica

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

DSolve[-y[x] + x*y'[x] + y'[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*}