Internal problem ID [4339]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1147.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(ln(diff(y(x),x))+a*(x*diff(y(x),x)-y(x)) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\ln \left (-\frac {1}{a x}\right )-1}{a} \\ y \left (x \right ) &= c_{1} x +\frac {\ln \left (c_{1} \right )}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 36
DSolve[Log[y'[x]]+a*( x*y'[x]-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (c_1)}{a}+c_1 x \\ y(x)\to \frac {\log \left (-\frac {1}{a x}\right )-1}{a} \\ \end{align*}