Internal problem ID [1037]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 x +y+\left (2 y+2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.132 (sec). Leaf size: 46
dsolve((2*x+y(x))+(2*y(x)+2*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 x}{4}+\frac {\sqrt {7}\, x \tan \left (\RootOf \left (\sqrt {7}\, \ln \left (\frac {7 x^{2}}{8}+\frac {7 x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{8}\right )+2 \sqrt {7}\, c_{1}+2 \textit {\_Z} \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 62
DSolve[(2*x+y[x])+(2*y[x]+2*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {ArcTan}\left (\frac {\frac {4 y(x)}{x}+3}{\sqrt {7}}\right )}{2 \sqrt {7}}+\frac {1}{4} \log \left (\frac {2 y(x)^2}{x^2}+\frac {3 y(x)}{x}+2\right )=-\frac {\log (x)}{2}+c_1,y(x)\right ] \]