83.8.7 problem 7

Internal problem ID [19133]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:04:55 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }+y \ln \left (y\right )&=x y \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 19

dsolve(x*diff(y(x),x)+y(x)*ln(y(x))=x*y(x)*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{\frac {\left (x -1\right ) {\mathrm e}^{x}-c_{1}}{x}} \]

✓ Solution by Mathematica

Time used: 0.460 (sec). Leaf size: 21

DSolve[x*D[y[x],x]+y[x]*Log[y[x]]==x*y[x]*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {e^x (x-1)+c_1}{x}} \]