Internal problem ID [3828]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1144.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\ln \left (y^{\prime }\right )+y^{\prime } x +a -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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 \relax (x ) = \ln \left (-\frac {1}{x}\right )+a -1 \\ y \relax (x ) = \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*}