20.3.26 problem Problem 33

Internal problem ID [3635]
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 33
Date solved : Tuesday, March 04, 2025 at 04:55:27 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 17

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

\[ y(x)\to x (-x+x \log (x)+c_1) \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 12

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

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