85.23.1 problem 2

Internal problem ID [22576]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 55
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:52:00 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: 0.020 (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: 0.151 (sec). Leaf size: 16

ode=x*D[y[x],{x,1}]==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: 0.429 (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)
 

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