60.1.4 problem 4

Internal problem ID [10018]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 08:04:21 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(y(x),x)+2*x*y(x)-x*exp(-x^2) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 24

ode=D[y[x],x] + 2*x*y[x] - x*Exp[-x^2]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \]

✓ Sympy. Time used: 0.253 (sec). Leaf size: 14

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

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