Internal problem ID [3166]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 420.
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 {y y^{\prime }+a x +b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.153 (sec). Leaf size: 94
dsolve(y(x)*diff(y(x),x)+a*x+b*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z}^{2}-{\mathrm e}^{\RootOf \left (x^{2} \left (-\left (\tanh ^{2}\left (\frac {\sqrt {b^{2}-4 a}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 b}\right )\right ) b^{2}+4 \left (\tanh ^{2}\left (\frac {\sqrt {b^{2}-4 a}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \relax (x )\right )}{2 b}\right )\right ) a +b^{2}+4 \,{\mathrm e}^{\textit {\_Z}}-4 a \right )\right )}+a +\textit {\_Z} b \right ) x \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 74
DSolve[y[x] y'[x]+a x+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (a+\frac {b y(x)}{x}+\frac {y(x)^2}{x^2}\right )-\frac {b \text {ArcTan}\left (\frac {b+\frac {2 y(x)}{x}}{\sqrt {4 a-b^2}}\right )}{\sqrt {4 a-b^2}}=-\log (x)+c_1,y(x)\right ] \]