73.7.50 problem 50

Internal problem ID [15129]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 50
Date solved : Thursday, March 13, 2025 at 05:47:17 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+3 x y&=6 \,{\mathrm e}^{-x^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x^2*diff(y(x),x)+3*x*y(x) = 6*exp(-x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-3 \,{\mathrm e}^{-x^{2}}+c_{1}}{x^{3}} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 21

ode=x^2*D[y[x],x]+3*x*y[x]==6*Exp[-x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.285 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + 3*x*y(x) - 6*exp(-x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - 3 e^{- x^{2}}}{x^{3}} \]