Internal problem ID [6122]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 13.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{3}-2 \left (y^{\prime }\right )^{2} y x +y^{2} y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.273 (sec). Leaf size: 81
dsolve(x^2*diff(y(x),x)^3-2*x*y(x)*diff(y(x),x)^2+y(x)^2*diff(y(x),x)+1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 \left (-2 x \right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {3 \left (-2 x \right )^{\frac {1}{3}}}{4}-\frac {3 i \sqrt {3}\, \left (-2 x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = -\frac {3 \left (-2 x \right )^{\frac {1}{3}}}{4}+\frac {3 i \sqrt {3}\, \left (-2 x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = c_{1} x -\frac {1}{\sqrt {-c_{1}}} \\ y \relax (x ) = c_{1} x +\frac {1}{\sqrt {-c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 97.887 (sec). Leaf size: 33909
DSolve[x^2*(y'[x])^3-2*x*y[x]*(y'[x])^2+y[x]^2*y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
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