81.11.22 problem 15-21

Internal problem ID [21646]
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 : 15-21
Date solved : Thursday, October 02, 2025 at 07:59:25 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = {\mathrm e}^{2 x} c_1 +\frac {3 \cos \left (x \right )}{5}+\frac {\sin \left (x \right )}{5}+{\mathrm e}^{x} c_2 \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {1}{5} \left (\sin (x)+3 \cos (x)+5 e^x \left (c_2 e^x+c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + \frac {\sin {\left (x \right )}}{5} + \frac {3 \cos {\left (x \right )}}{5} \]