Internal problem ID [3247]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 501.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (a x +b y\right ) y^{\prime }+b x +a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 85
dsolve((a*x+b*y(x))*diff(y(x),x)+b*x+a*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {c_{1} a x -\sqrt {a^{2} x^{2} c_{1}^{2}-b^{2} x^{2} c_{1}^{2}+b}}{b c_{1}} \\ y \relax (x ) = -\frac {c_{1} a x +\sqrt {a^{2} x^{2} c_{1}^{2}-b^{2} x^{2} c_{1}^{2}+b}}{b c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 14.243 (sec). Leaf size: 135
DSolve[(a x+b y[x])y'[x]+b x+a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a x+\sqrt {x^2 (a-b) (a+b)+b e^{2 c_1}}}{b} \\ y(x)\to \frac {-a x+\sqrt {x^2 (a-b) (a+b)+b e^{2 c_1}}}{b} \\ y(x)\to -\frac {\sqrt {x^2 (a-b) (a+b)}+a x}{b} \\ y(x)\to \frac {\sqrt {x^2 (a-b) (a+b)}-a x}{b} \\ \end{align*}