44.6.9 problem 9

Internal problem ID [7153]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 9
Date solved : Wednesday, March 05, 2025 at 04:19:02 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = x \left (-\cos \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.357 (sec). Leaf size: 8

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

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