23.1.22 problem 2(L)

Internal problem ID [4112]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(L)
Date solved : Monday, January 27, 2025 at 08:09:13 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x -y}{y+2 x} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.408 (sec). Leaf size: 66

dsolve([diff(y(x),x)=(2*x-y(x))/(2*x+y(x)),y(2) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (-2 \sqrt {17}\, \operatorname {arctanh}\left (\frac {5 \sqrt {17}}{17}\right )+2 \sqrt {17}\, \operatorname {arctanh}\left (\frac {\left (3 x +2 \textit {\_Z} \right ) \sqrt {17}}{17 x}\right )-34 \ln \left (x \right )+51 \ln \left (2\right )-17 \ln \left (\frac {\textit {\_Z}^{2}+3 x \textit {\_Z} -2 x^{2}}{x^{2}}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 137

DSolve[{D[y[x],x]==(2*x-y[x])/(2*x+y[x]),y[2]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{34} \left (\left (17+\sqrt {17}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {17}-3\right )-\left (\sqrt {17}-17\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {17}+3\right )\right )=-\log (x)+\frac {1}{34} i \left (17+\sqrt {17}\right ) \pi +\frac {1}{34} \left (34 \log (2)+17 \log \left (5-\sqrt {17}\right )+\sqrt {17} \log \left (5-\sqrt {17}\right )+17 \log \left (5+\sqrt {17}\right )-\sqrt {17} \log \left (5+\sqrt {17}\right )\right ),y(x)\right ] \]