88.9.10 problem 10

Internal problem ID [24030]
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 2. Differential equations of first order. Exercise at page 48
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:54:42 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y x&=x^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x)-x*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 24

ode=D[y[x],{x,1}]-x*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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