20.1.29 problem Problem 37

Internal problem ID [3586]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 37
Date solved : Sunday, March 30, 2025 at 01:53:28 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 18

ode:=diff(y(x),x) = x^2*ln(x); 
ic:=y(1) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}+\frac {19}{9} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

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

\[ y(x)\to \frac {1}{9} \left (-x^3+3 x^3 \log (x)+19\right ) \]

✓ Sympy. Time used: 0.160 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*log(x) + Derivative(y(x), x),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{3} \log {\left (x \right )}}{3} - \frac {x^{3}}{9} + \frac {19}{9} \]