20.3.13 problem Problem 13

Internal problem ID [3622]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 13
Date solved : Tuesday, March 04, 2025 at 04:55:05 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y \left (x \right ) = x^{3} \ln \left (x \right )-\frac {x^{3}}{2}+c_{1} x \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 23

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

\[ y(x)\to -\frac {x^3}{2}+x^3 \log (x)+c_1 x \]

✓ Sympy. Time used: 0.212 (sec). Leaf size: 17

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

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