88.13.4 problem 4

Internal problem ID [24087]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 86
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:59:04 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (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: 0.036 (sec). Leaf size: 24

ode=D[y[x],{x,1}]-x*y[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: 0.162 (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)
 

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