29.18.25 problem 501

Internal problem ID [5099]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 501
Date solved : Monday, January 27, 2025 at 10:11:10 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 75

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

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

✓ Solution by Mathematica

Time used: 15.904 (sec). Leaf size: 143

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

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