Internal problem ID [6131]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 23.
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}-\left (y^{\prime }\right )^{2}+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.222 (sec). Leaf size: 33
dsolve(diff(y(x),x)^3-diff(y(x),x)^2+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}^{3}-c_{1}^{2}+c_{1} x \\ y \relax (x ) = \frac {x}{3}-\frac {2}{27}+\left (3 x -1\right )^{\frac {3}{2}} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 74
DSolve[y'[x]^3-y'[x]^2+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+(-1+c_1) c_1) \\ y(x)\to \frac {1}{27} \left (9 x-2 \left (\sqrt {-(3 x-1)^3}+1\right )\right ) \\ y(x)\to \frac {1}{27} \left (9 x+2 \sqrt {-(3 x-1)^3}-2\right ) \\ \end{align*}