50.3.12 problem 2(b)

Internal problem ID [7836]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 2(b)
Date solved : Wednesday, March 05, 2025 at 05:07:28 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 18

ode:=diff(y(x),x)-2*x*y(x) = 6*x*exp(x^2); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 23

ode=D[y[x],x]-2*x*y[x]==6*x*Exp[x^2]; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x^2-1} \left (3 e \left (x^2-1\right )+1\right ) \]

✓ Sympy. Time used: 0.258 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) - 6*x*exp(x**2) + Derivative(y(x), x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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