29.19.8 problem 521

Internal problem ID [5117]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 521
Date solved : Monday, January 27, 2025 at 10:12:11 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 50

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

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