60.1.338 problem 345

Internal problem ID [10352]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 345
Date solved : Wednesday, March 05, 2025 at 10:32:48 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 36

ode:=x*(2*x^2*y(x)*ln(y(x))+1)*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} \,x^{2} {\mathrm e}^{2 \textit {\_Z}}-x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x^{2}+2 \,{\mathrm e}^{\textit {\_Z}}\right )} \]

✓ Mathematica. Time used: 0.178 (sec). Leaf size: 35

ode=-2*y[x] + x*(1 + 2*x^2*Log[y[x]]*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)}{x^2}+2 \left (\frac {1}{2} y(x)^2 \log (y(x))-\frac {y(x)^2}{4}\right )=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.909 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(2*x**2*y(x)*log(y(x)) + 1)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - \frac {y^{2}{\left (x \right )} \log {\left (y{\left (x \right )} \right )}}{2} + \frac {y^{2}{\left (x \right )}}{4} - \frac {y{\left (x \right )}}{2 x^{2}} = 0 \]