81.11.4 problem 15-3

Internal problem ID [21628]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-3
Date solved : Thursday, October 02, 2025 at 07:59:10 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=x^{3} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 35

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

\[ y = -\frac {\left (\left (2 x^{2}-4 c_1 \right ) {\mathrm e}^{4 x}+x^{3}+\frac {3 x^{2}}{4}+\frac {3 x}{8}+\frac {3}{32}\right ) {\mathrm e}^{x}}{4} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to -\frac {1}{128} e^x \left (32 x^3+8 \left (8 e^{4 x}+3\right ) x^2+12 x-128 c_1 e^{4 x}+3\right ) \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = \left (- \frac {x^{3}}{4} - \frac {3 x^{2}}{16} - \frac {3 x}{32} + \left (C_{1} - \frac {x^{2}}{2}\right ) e^{4 x} - \frac {3}{128}\right ) e^{x} \]