78.2.12 problem 5.b

Internal problem ID [20964]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 5.b
Date solved : Thursday, October 02, 2025 at 07:00:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=5+10 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 5+10*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 5+\left (c_1 x +c_2 \right ) {\mathrm e}^{-x}-\frac {8 \cos \left (2 x \right )}{5}-\frac {6 \sin \left (2 x \right )}{5} \]

✓ Mathematica. Time used: 0.193 (sec). Leaf size: 40

ode=D[y[x],{x,2}]+2*D[y[x],x]+y[x]==5+10*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {6}{5} \sin (2 x)-\frac {8}{5} \cos (2 x)+e^{-x} \left (5 e^x+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 10*sin(2*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} - \frac {6 \sin {\left (2 x \right )}}{5} - \frac {8 \cos {\left (2 x \right )}}{5} + 5 \]