87.17.18 problem 18

Internal problem ID [23610]
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 : 18
Date solved : Thursday, October 02, 2025 at 09:43:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

\[ y = {\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 +\frac {{\mathrm e}^{-x} \left (\cos \left (x \right )-\sin \left (x \right )\right )}{10} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to c_1 e^x+c_2 e^{2 x}+\frac {1}{10} e^{-x} (\cos (x)-\sin (x)) \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + \frac {\left (- \sin {\left (x \right )} + \cos {\left (x \right )}\right ) e^{- x}}{10} \]