Internal problem ID [6125]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 16.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-2 x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 496
dsolve(diff(y(x),x)^3-2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} -\frac {c_{1}}{\left (\frac {\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}+24 x}{\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}+24 x \right )^{2}}{96 \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}} = 0 \\ -\frac {c_{1}}{\left (\frac {i \sqrt {3}\, \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 i x \sqrt {3}-\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (i \sqrt {3}\, \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 i x \sqrt {3}-\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 x \right )^{2}}{384 \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}} = 0 \\ -\frac {12^{\frac {2}{3}} c_{1}}{\left (\frac {-i \sqrt {3}\, \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}+24 i x \sqrt {3}-\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {1}{3}}}\right )^{\frac {2}{3}}}+x -\frac {\left (i \sqrt {3}\, \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}-24 i x \sqrt {3}+\left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}+24 x \right )^{2}}{384 \left (108 y \relax (x )+12 \sqrt {-96 x^{3}+81 y \relax (x )^{2}}\right )^{\frac {2}{3}}} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3-2*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out