Internal problem ID [6883]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 22.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {\left (y^{\prime }+1\right )^{2} \left (y-y^{\prime } x \right )=1} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 106
dsolve((diff(y(x),x)+1)^2*(y(x)-diff(y(x),x)*x)=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {3 \,2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{2}-x y \left (x \right ) = -\frac {3 \,2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-\frac {3 i \sqrt {3}\, 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-x y \left (x \right ) = -\frac {3 \,2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}+\frac {3 i \sqrt {3}\, 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-x y \left (x \right ) = \frac {\left (c_{1}^{3}+2 c_{1}^{2}+c_{1} \right ) x}{\left (1+c_{1} \right )^{2}}+\frac {1}{\left (1+c_{1} \right )^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 102
DSolve[(y'[x]+1)^2*(y[x]-y'[x]*x)==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\frac {1}{(1+c_1){}^2} y(x)\to \frac {3 x^{2/3}}{2^{2/3}}-x y(x)\to -x+\frac {3 i \left (\sqrt {3}+i\right ) x^{2/3}}{2\ 2^{2/3}} y(x)\to -x-\frac {3 \left (1+i \sqrt {3}\right ) x^{2/3}}{2\ 2^{2/3}} \end{align*}