68.5.19 problem 19

Internal problem ID [17270]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 19
Date solved : Thursday, October 02, 2025 at 02:00:32 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

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

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

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

✓ Sympy. Time used: 0.167 (sec). Leaf size: 12

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

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