75.6.11 problem 135

Internal problem ID [16696]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 135
Date solved : Monday, March 31, 2025 at 03:06:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+c_1 \right )} \]

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 19

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

\[ \text {Solve}\left [x=y(x) \log (y(x))+\frac {c_1}{y(x)},y(x)\right ] \]

✓ Sympy. Time used: 0.856 (sec). Leaf size: 17

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

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