69.6.8 problem 132

Internal problem ID [18051]
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 : 132
Date solved : Thursday, October 02, 2025 at 02:36:14 PM
CAS classification : [_linear]

\begin{align*} x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(x),x)*x*ln(x)-y(x) = 3*x^3*ln(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{3}+c_1 \right ) \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 14

ode=D[y[x],x]*x*Log[x]-y[x]==3*x^3*(Log[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (x^3+c_1\right ) \log (x) \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3*log(x)**2 + x*log(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x^{3}\right ) \log {\left (x \right )} \]