87.16.17 problem 17

Internal problem ID [23586]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:43:14 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = -\frac {{\mathrm e}^{-5 x} c_1}{5}-\frac {\sin \left (x \right )}{26}-\frac {5 \cos \left (x \right )}{26}+c_2 \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to -\frac {\sin (x)}{26}-\frac {5 \cos (x)}{26}-\frac {1}{5} c_1 e^{-5 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 22

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

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