Internal problem ID [2663]
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: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 56
dsolve((2*x*y(x))+(x^2+2*x*y(x)+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -x +\sqrt {2}\, x \tan \left (\RootOf \left (2 \sqrt {2}\, \ln \left (-x^{3} \left (\sqrt {2}-2 \tan \left (\textit {\_Z} \right )\right ) \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )\right )+\sqrt {2}\, \ln \relax (2)+6 \sqrt {2}\, c_{1}+4 \textit {\_Z} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 62
DSolve[(2*x*y[x])+(x^2+2*x*y[x]+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{3} \left (\sqrt {2} \text {ArcTan}\left (\frac {\frac {y(x)}{x}+1}{\sqrt {2}}\right )+\log \left (\frac {y(x)^2}{x^2}+\frac {2 y(x)}{x}+3\right )+\log \left (\frac {y(x)}{x}\right )\right )=-\log (x)+c_1,y(x)\right ] \]