87.17.2 problem 2

Internal problem ID [23594]
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 127
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:43:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-y(x) = exp(x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +\frac {\left (2 x +4 c_1 -1\right ) {\mathrm e}^{x}}{4}-\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to -\frac {\sin (x)}{2}+e^x \left (\frac {x}{2}-\frac {1}{4}+c_1\right )+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 20

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

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