60.1.119 problem 120

Internal problem ID [10133]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 120
Date solved : Tuesday, January 28, 2025 at 04:25:57 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve(x*diff(y(x),x) - y(x)*(x*ln(x^2/y(x))+2)=0,y(x), singsol=all)
 

\[ y = x^{2} {\mathrm e}^{-c_{1} {\mathrm e}^{-x}} \]

✓ Solution by Mathematica

Time used: 0.272 (sec). Leaf size: 20

DSolve[x*D[y[x],x] - y[x]*(x*Log[x^2/y[x]]+2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 e^{-2 c_1 e^{-x}} \]