73.15.12 problem 22.5 (b)

Internal problem ID [15364]
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, March 13, 2025 at 05:56:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\[ y = -\frac {{\mathrm e}^{-5 x} \left (\left (x^{3}+\frac {12}{5} x^{2}+\frac {126}{25} x +\frac {624}{125}\right ) {\mathrm e}^{5 x}-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{1} \right )}{5} \]

✓ Mathematica. Time used: 0.014 (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]
 

\[ y(x)\to \frac {1}{625} \left (-125 x^3-300 x^2-630 x-624\right )+c_1 e^{-5 x}+c_2 e^x \]

✓ Sympy. Time used: 0.217 (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)
 

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