Internal problem ID [6875]
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]
\[ \boxed {x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 82
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 \left (x \right ) &= \frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {1}{3}}}{2} \\ y \left (x \right ) &= -\frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4} \\ y \left (x \right ) &= c_{1} x -\frac {1}{\sqrt {-c_{1}}} \\ y \left (x \right ) &= c_{1} x +\frac {1}{\sqrt {-c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 66.431 (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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