29.20.2 problem 547

Internal problem ID [5143]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 547
Date solved : Monday, January 27, 2025 at 10:14:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 4.770 (sec). Leaf size: 92

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

\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {x \left (x-4 e^{c_1}\right )}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {x \left (x-4 e^{c_1}\right )}\right ) \\ y(x)\to 0 \\ y(x)\to \frac {1}{2} \left (x-\sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {x^2}+x\right ) \\ \end{align*}