29.17.5 problem 464

Internal problem ID [5062]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 464
Date solved : Monday, January 27, 2025 at 10:07:11 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.058 (sec). Leaf size: 51

dsolve((x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {c_{1} x -\sqrt {5 c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ y \left (x \right ) &= \frac {c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.467 (sec). Leaf size: 102

DSolve[(x-2 y[x])D[y[x],x]+2 x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+x\right ) \\ \end{align*}