81.11.5 problem 15-4

Internal problem ID [21629]
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 : 15-4
Date solved : Thursday, October 02, 2025 at 07:59:12 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(y(x),x)-5*y(x) = (x-1)*sin(x)+(1+x)*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} c_1 +\frac {\left (-78 x -69\right ) \cos \left (x \right )}{338}+\frac {\left (-52 x +71\right ) \sin \left (x \right )}{338} \]

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 36

ode=D[y[x],x]-5*y[x]==(x-1)*Sin[x]+(x+1)*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{338} ((71-52 x) \sin (x)-3 (26 x+23) \cos (x))+c_1 e^{5 x} \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 70

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x)*sin(x) - (x + 1)*cos(x) - 5*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{5 x} - \frac {5 \sqrt {2} x \sin {\left (x + \frac {\pi }{4} \right )}}{26} - \frac {\sqrt {2} x \cos {\left (x + \frac {\pi }{4} \right )}}{26} + \frac {\sqrt {2} \sin {\left (x + \frac {\pi }{4} \right )}}{338} - \frac {35 \sqrt {2} \cos {\left (x + \frac {\pi }{4} \right )}}{169} \]