81.6.12 problem 7-12

Internal problem ID [21558]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-12
Date solved : Thursday, October 02, 2025 at 07:48:09 PM
CAS classification : [_separable]

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

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

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

\[ y = -\frac {1}{2}+{\mathrm e}^{x^{2}} c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to -\frac {1}{2}+c_1 e^{x^2}\\ y(x)&\to -\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 12

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

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