Internal problem ID [3232]
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`]]
\[ \boxed {y \left (y-2 x y^{\prime }\right )^{3}-{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.156 (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 \left (x \right ) &= -\frac {\sqrt {3}}{9 x} \\ y \left (x \right ) &= \frac {\sqrt {3}}{9 x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +24 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{36 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}+\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}-\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} -48 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}-72 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}+\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}-24 \textit {\_a}^{2}+2 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}}+1}d \textit {\_a} \right )\right )}{x} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +48 \left (\int _{}^{\textit {\_Z}}\frac {\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}}{i \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}} \sqrt {3}+24 i \sqrt {3}\, \textit {\_a}^{2}+72 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {1}{3}} \textit {\_a}^{2}-i \sqrt {3}-\left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+36 \textit {\_a}^{2}-1\right )^{\frac {2}{3}}+24 \textit {\_a}^{2}-2 \left (-216 \textit {\_a}^{4}+24 \textit {\_a}^{3} \sqrt {81 \textit {\_a}^{2}-3}+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