Internal problem ID [2514]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(L).
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 {y^{\prime }-\frac {2 x -y}{y+2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 2] \end {align*}
✓ Solution by Maple
Time used: 1.639 (sec). Leaf size: 66
dsolve([diff(y(x),x)=(2*x-y(x))/(2*x+y(x)),y(2) = 2],y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (2 \sqrt {17}\, \arctanh \left (\frac {5 \sqrt {17}}{17}\right )-2 \sqrt {17}\, \arctanh \left (\frac {\left (3 x +2 \textit {\_Z} \right ) \sqrt {17}}{17 x}\right )+34 \ln \relax (x )+17 \ln \left (\frac {\textit {\_Z}^{2}+3 x \textit {\_Z} -2 x^{2}}{x^{2}}\right )-51 \ln \relax (2)\right ) \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 137
DSolve[{y'[x]==(2*x-y[x])/(2*x+y[x]),y[2]==2},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{34} \left (\left (17+\sqrt {17}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {17}-3\right )-\left (\sqrt {17}-17\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {17}+3\right )\right )=-\log (x)+\frac {1}{34} i \left (17+\sqrt {17}\right ) \pi +\frac {1}{34} \left (34 \log (2)+17 \log \left (5-\sqrt {17}\right )+\sqrt {17} \log \left (5-\sqrt {17}\right )+17 \log \left (5+\sqrt {17}\right )-\sqrt {17} \log \left (5+\sqrt {17}\right )\right ),y(x)\right ] \]