88.13.5 problem 5

Internal problem ID [24088]
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 : 5
Date solved : Thursday, October 02, 2025 at 09:59:06 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y x&=-x^{5}+4 x^{3} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 16

ode:=diff(y(x),x)-x*y(x) = -x^5+4*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{4}+{\mathrm e}^{\frac {x^{2}}{2}} c_1 \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 21

ode=D[y[x],{x,1}]-x*y[x]==4*x^3-x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^4+c_1 e^{\frac {x^2}{2}} \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5 - 4*x**3 - x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x^{2}}{2}} + x^{4} \]