Internal problem ID [3755]
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`]]
\[ \boxed {\left (x a +y b \right ) y^{\prime }+a y=-b x} \]
✓ Solution by Maple
Time used: 0.032 (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 \left (x \right ) = -\frac {c_{1} a x -\sqrt {a^{2} c_{1}^{2} x^{2}-b^{2} c_{1}^{2} x^{2}+b}}{b c_{1}} y \left (x \right ) = -\frac {c_{1} a x +\sqrt {a^{2} c_{1}^{2} x^{2}-b^{2} c_{1}^{2} x^{2}+b}}{b c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 15.858 (sec). Leaf size: 143
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 {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*}