54.2.14 problem 16

Internal problem ID [8546]
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
Date solved : Monday, January 27, 2025 at 04:13:33 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 442

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+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x -\frac {{\left (\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x \right )}^{2}}{96 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ -\frac {c_{1}}{{\left (\frac {i \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}} \sqrt {3}-24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (-\frac {\left (\sqrt {3}+i\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+x \left (-i+\sqrt {3}\right )\right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ -\frac {12^{{2}/{3}} c_{1}}{{\left (\frac {-i \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}} \sqrt {3}+24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (\frac {\left (i-\sqrt {3}\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+\left (\sqrt {3}+i\right ) x \right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(D[y[x],x])^3-2*x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out