Internal problem ID [4336]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1144.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {\ln \left (y^{\prime }\right )+x y^{\prime }-y=-a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \ln \left (-\frac {1}{x}\right )+a -1 y \left (x \right ) = \ln \left (c_{1} \right )+c_{1} x +a \end{align*}
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 27
DSolve[Log[y'[x]]+x y'[x]+ a ==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a+c_1 x+\log (c_1) y(x)\to a+\log \left (-\frac {1}{x}\right )-1 \end{align*}