8.4.4 problem 4

Internal problem ID [707]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 4
Date solved : Tuesday, March 04, 2025 at 11:33:26 AM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 15

ode=-2*x*y[x]+D[y[x],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: 0.208 (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)
 

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