40.9.12 problem 22

Internal problem ID [6722]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 22
Date solved : Sunday, March 30, 2025 at 11:20:37 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{-x}\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = sin(exp(-x)); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Sin[Exp[-x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (-e^x \sin \left (e^{-x}\right )+c_2 e^x+c_1\right ) \]

✓ Sympy. Time used: 5.563 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - sin(exp(-x)) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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