85.49.2 problem 1 (b)

Internal problem ID [22803]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 194
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 09:14:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 4*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{-x}-\frac {16 \cos \left (2 x \right )}{25}-\frac {12 \sin \left (2 x \right )}{25} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+2*D[y[x],{x,1}]+y[x]==4*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {12}{25} \sin (2 x)-\frac {16}{25} \cos (2 x)+e^{-x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 4*sin(2*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} - \frac {12 \sin {\left (2 x \right )}}{25} - \frac {16 \cos {\left (2 x \right )}}{25} \]