60.1.561 problem 564

Internal problem ID [10575]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 564
Date solved : Monday, January 27, 2025 at 09:16:20 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} \ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (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 &= \frac {\ln \left (-\frac {1}{a x}\right )-1}{a} \\ y &= c_{1} x +\frac {\ln \left (c_{1} \right )}{a} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 36

DSolve[Log[D[y[x],x]] + a*(-y[x] + x*D[y[x],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*}