7.4.4 problem 4

Internal problem ID [76]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 4
Date solved : Saturday, March 29, 2025 at 04:30:15 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \left (x +c_1 \right ) {\mathrm e}^{x^{2}} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.222 (sec). Leaf size: 10

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

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