88.13.3 problem 3

Internal problem ID [24086]
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 : 3
Date solved : Thursday, October 02, 2025 at 09:59:02 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = -\frac {9 x^{2}}{25}-\frac {3 x^{3}}{5}-\frac {118 x}{125}-\frac {118}{625}+{\mathrm e}^{5 x} c_1 \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {1}{625} \left (-375 x^3-225 x^2-590 x-118\right )+c_1 e^{5 x} \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} e^{5 x} - \frac {3 x^{3}}{5} - \frac {9 x^{2}}{25} - \frac {118 x}{125} - \frac {118}{625} \]