60.1.345 problem 346

Internal problem ID [10359]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 346
Date solved : Monday, January 27, 2025 at 07:30:31 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 19

dsolve(x*(y(x)*ln(x*y(x))+y(x)-a*x)*diff(y(x),x)-y(x)*(a*x*ln(x*y(x))-y(x)+a*x) = 0,y(x), singsol=all)
 

\[ \left (x y\right )^{-a x +y}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.327 (sec). Leaf size: 24

DSolve[-((a*x + a*x*Log[x*y[x]] - y[x])*y[x]) + x*(-(a*x) + y[x] + Log[x*y[x]]*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)] \]