Internal problem ID [3245]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 499.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (a x +b y\right ) y^{\prime }+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 98
dsolve((a*x+b*y(x))*diff(y(x),x)+x = 0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (b \,\textit {\_Z}^{2}-{\mathrm e}^{\RootOf \left (x^{2} \left (\left (\tanh ^{2}\left (\frac {\sqrt {a^{2}-4 b}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 a}\right )\right ) a^{2}-4 \left (\tanh ^{2}\left (\frac {\sqrt {a^{2}-4 b}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 a}\right )\right ) b -4 b \,{\mathrm e}^{\textit {\_Z}}-a^{2}+4 b \right )\right )}+1+a \textit {\_Z} \right ) x \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 75
DSolve[(a x+b y[x])y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {a \text {ArcTan}\left (\frac {a+\frac {2 b y(x)}{x}}{\sqrt {4 b-a^2}}\right )}{\sqrt {4 b-a^2}}+\frac {1}{2} \log \left (\frac {a y(x)}{x}+\frac {b y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]