Internal problem ID [3783]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1072.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{3}-3 x y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.231 (sec). Leaf size: 607
dsolve(y(x)*diff(y(x),x)^3-3*x*diff(y(x),x)+3*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \RootOf \left (-2 \ln \relax (x )+\int _{}^{\textit {\_Z}}\frac {-2 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}} \textit {\_a}^{3}-8 \textit {\_a}^{3}+\left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {2}{3}}+2 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}+4}{\textit {\_a}^{4} \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}}d \textit {\_a} +2 c_{1}\right ) x \\ y \relax (x ) = \RootOf \left (-4 \ln \relax (x )+\int _{}^{\textit {\_Z}}\frac {8 i \sqrt {3}\, \textit {\_a}^{3}+i \sqrt {3}\, \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {2}{3}}-4 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}} \textit {\_a}^{3}+8 \textit {\_a}^{3}-4 i \sqrt {3}-\left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {2}{3}}+4 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}-4}{\textit {\_a}^{4} \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}}d \textit {\_a} +4 c_{1}\right ) x \\ y \relax (x ) = \RootOf \left (-4 \ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {8 i \sqrt {3}\, \textit {\_a}^{3}+i \sqrt {3}\, \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {2}{3}}+4 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}} \textit {\_a}^{3}-8 \textit {\_a}^{3}-4 i \sqrt {3}+\left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {2}{3}}-4 \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}+4}{\textit {\_a}^{4} \left (4 \sqrt {\frac {9 \textit {\_a}^{3}-4}{\textit {\_a}}}\, \textit {\_a}^{5}+12 \textit {\_a}^{6}-24 \textit {\_a}^{3}+8\right )^{\frac {1}{3}}}d \textit {\_a} \right )+4 c_{1}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 56.979 (sec). Leaf size: 8706
DSolve[y[x] (y'[x])^3 -3 x y'[x] + 3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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