Internal problem ID [4292]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1073.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 740
dsolve(2*y(x)*diff(y(x),x)^3-3*x*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {2^{\frac {2}{3}} x}{2} y \left (x \right ) = \left (-\frac {2^{\frac {2}{3}}}{4}-\frac {i \sqrt {3}\, 2^{\frac {2}{3}}}{4}\right ) x y \left (x \right ) = \left (-\frac {2^{\frac {2}{3}}}{4}+\frac {i \sqrt {3}\, 2^{\frac {2}{3}}}{4}\right ) x y \left (x \right ) = 0 y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {2 {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}} \textit {\_a}^{3}+2 \textit {\_a}^{3}-{\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {2}{3}}-{\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}-1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right ) {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}}d \textit {\_a} +c_{1} \right ) x y \left (x \right ) = \operatorname {RootOf}\left (-2 \ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {2 i \sqrt {3}\, \textit {\_a}^{3}+i \sqrt {3}\, {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {2}{3}}-4 {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}} \textit {\_a}^{3}+2 \textit {\_a}^{3}-i \sqrt {3}-{\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {2}{3}}+2 {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}-1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right ) {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}}d \textit {\_a} +2 c_{1} \right ) x y \left (x \right ) = \operatorname {RootOf}\left (-2 \ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {2 i \sqrt {3}\, \textit {\_a}^{3}+i \sqrt {3}\, {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {2}{3}}+4 {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}} \textit {\_a}^{3}-2 \textit {\_a}^{3}-i \sqrt {3}+{\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {2}{3}}-2 {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}+1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right ) {\left (\left (\sqrt {2}\, \sqrt {\frac {1}{\textit {\_a} \left (2 \textit {\_a}^{3}-1\right )}}\, \textit {\_a}^{2}+1\right ) \left (2 \textit {\_a}^{3}-1\right )^{2}\right )}^{\frac {1}{3}}}d \textit {\_a} \right )+2 c_{1} \right ) x \end{align*}
✓ Solution by Mathematica
Time used: 172.826 (sec). Leaf size: 10331
DSolve[2 y[x] (y'[x])^3 -3 x y'[x]+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display