Internal problem ID [3248]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 502.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _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: 0.059 (sec). Leaf size: 64
dsolve((a*x+b*y(x))*diff(y(x),x) = b*x+a*y(x),y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{\RootOf \left ({\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\frac {2 c_{1} b}{a -b}} {\mathrm e}^{\frac {a \textit {\_Z}}{a -b}} {\mathrm e}^{\frac {\textit {\_Z} b}{a -b}} x^{\frac {2 b}{a -b}}+2\right )}+x \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 48
DSolve[(a x+b y[x])y'[x]==b x+a y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} (a+b) \log \left (1-\frac {y(x)}{x}\right )+\frac {1}{2} (b-a) \log \left (\frac {y(x)}{x}+1\right )=-b \log (x)+c_1,y(x)\right ] \]