60.1.222 problem 223

Internal problem ID [10236]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 223
Date solved : Monday, January 27, 2025 at 06:40:48 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.460 (sec). Leaf size: 102

DSolve[(2*y[x]-x)*D[y[x],x]-y[x]-2*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*}