81.1.6 problem 5

Internal problem ID [18601]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:03:49 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 57

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

\begin{align*} y(x)\to c_1 \left (x+1-c_1{}^2\right ) \\ y(x)\to -\frac {2 (x+1)^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 (x+1)^{3/2}}{3 \sqrt {3}} \\ \end{align*}