67.15.12 problem 22.5 (b)

Internal problem ID [16730]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.5 (b)
Date solved : Thursday, October 02, 2025 at 01:38:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\[ y = {\mathrm e}^{-5 x} c_2 +{\mathrm e}^{x} c_1 -\frac {x^{3}}{5}-\frac {12 x^{2}}{25}-\frac {126 x}{125}-\frac {624}{625} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 39

ode=D[y[x],{x,2}]+4*D[y[x],x]-5*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{625} \left (-125 x^3-300 x^2-630 x-624\right )+c_1 e^{-5 x}+c_2 e^x \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - 5*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{x} - \frac {x^{3}}{5} - \frac {12 x^{2}}{25} - \frac {126 x}{125} - \frac {624}{625} \]