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]
\[ \boxed {\left (y^{\prime }+1\right )^{2} \left (y-x y^{\prime }\right )=1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 93
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 {\left (-3 i \sqrt {3}-3\right ) 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-x \\ y \left (x \right ) &= \frac {\left (3 i \sqrt {3}-3\right ) 2^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-x \\ y \left (x \right ) &= \frac {c_{1}^{3} x +2 c_{1}^{2} x +c_{1} x +1}{\left (c_{1} +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*}