Internal problem ID [3753]
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]
\[ \boxed {\left (a x +y b \right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 63
dsolve((a*x+b*y(x))*diff(y(x),x)+x = 0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z}^{2} b -{\mathrm e}^{\operatorname {RootOf}\left (\left (4 \,{\mathrm e}^{\textit {\_Z}} b {\cosh \left (\frac {\sqrt {a^{2}-4 b}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )}^{2}+a^{2}-4 b \right ) x^{2}\right )}+1+a \textit {\_Z} \right ) x \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 75
DSolve[(a x+b y[x])y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {a \arctan \left (\frac {a+\frac {2 b y(x)}{x}}{\sqrt {4 b-a^2}}\right )}{\sqrt {4 b-a^2}}+\frac {1}{2} \log \left (\frac {a y(x)}{x}+\frac {b y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]