72.6.17 problem 7

Internal problem ID [19471]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 7
Date solved : Thursday, October 02, 2025 at 04:29:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 12

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

\[ y = {\mathrm e}^{x \left (c_1 +2 x \right )} \]

✓ Mathematica. Time used: 0.156 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to e^{2 x (x+2 c_1)} \end{align*}

✓ Sympy. Time used: 0.419 (sec). Leaf size: 14

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

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