Internal problem ID [3743]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1026.
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}-y^{\prime } x +a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 1223
dsolve(diff(y(x),x)^3-x*diff(y(x),x)+a*y(x) = 0,y(x), singsol=all)
\begin{align*} \frac {c_{1} \left (48 \left (\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x -\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 x}{12 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} a -72 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x -\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 x}{12 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x -\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-144 i \sqrt {3}\, x^{2}+\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-48 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x +144 x^{2}}{24 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0 \\ \frac {c_{1} \left (-24 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{6 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} a +36 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (\frac {\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{6 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x +\frac {\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {4}{3}}+24 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x +144 x^{2}}{12 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0 \\ \frac {c_{1} \left (-48 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (-\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x +\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{12 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}} a +72 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (-\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}-12 i \sqrt {3}\, x +\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}+12 x}{12 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {1}{3}}}\right )^{\frac {1}{a -1}}\right )}{\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}}}+x +\frac {i \sqrt {3}\, \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {4}{3}}-144 i \sqrt {3}\, x^{2}-\left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {4}{3}}+48 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} x -144 x^{2}}{24 \left (-108 a y \relax (x )+12 \sqrt {81 a^{2} y \relax (x )^{2}-12 x^{3}}\right )^{\frac {2}{3}} \left (2 a -3\right )} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3 -x y'[x]+a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out