Internal problem ID [2723]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 90.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y \left (y-2 y^{\prime } x \right )^{3}-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 577
dsolve(y(x)* (y(x)-2*x*diff(y(x),x))^3= (diff(y(x),x))^2 ,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {3}}{9 x} \\ y \relax (x ) = \frac {\sqrt {3}}{9 x} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}+24 \left (\int _{}^{\textit {\_Z}}\frac {\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{36 \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}+\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}-\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}-48 \left (\int _{}^{\textit {\_Z}}\frac {\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}-72 \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}+\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}+2 \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}+48 \left (\int _{}^{\textit {\_Z}}\frac {\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}+72 \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}-\left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}+24 \textit {\_a}^{2}-2 \left (24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}-216 \textit {\_a}^{4}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}-1}d \textit {\_a} \right )\right )}{x} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*(y[x]-2*x*y'[x])^3== (y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
Timed out