35.8.17 problem 17

Internal problem ID [6224]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 17
Date solved : Monday, January 27, 2025 at 01:48:40 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.461 (sec). Leaf size: 94

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

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