Internal problem ID [6878]
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]
\[ \boxed {{y^{\prime }}^{3}-2 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 450
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 \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )}^{\frac {2}{3}}}+x -\frac {{\left (\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 x \right )}^{2}}{96 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}} &= 0 \\ -\frac {c_{1}}{{\left (\frac {i \sqrt {3}\, \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 i \sqrt {3}\, x -\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )}^{\frac {2}{3}}}+x +\frac {3 {\left (-\frac {\left (\sqrt {3}+i\right ) \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}}{24}+x \left (-i+\sqrt {3}\right )\right )}^{2}}{2 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}} &= 0 \\ -\frac {12^{\frac {2}{3}} c_{1}}{{\left (\frac {-i \sqrt {3}\, \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}+24 i \sqrt {3}\, x -\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}-24 x}{\left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {1}{3}}}\right )}^{\frac {2}{3}}}+x +\frac {3 {\left (\frac {\left (i-\sqrt {3}\right ) \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{2}}\right )^{\frac {2}{3}}}{24}+x \left (\sqrt {3}+i\right )\right )}^{2}}{2 \left (108 y \left (x \right )+12 \sqrt {-96 x^{3}+81 y \left (x \right )^{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