78.2.36 problem 15.b

Internal problem ID [20988]
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 : 15.b
Date solved : Thursday, October 02, 2025 at 07:01:07 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)+y(x) = 2*sin(3*x); 
ic:=[y(0) = 5, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sin \left (x \right )^{3}+5 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 14

ode=D[y[x],{x,2}]+y[x]==2*Sin[3*x]; 
ic={y[0]==5,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin ^3(x)+5 \cos (x) \end{align*}

✓ Sympy. Time used: 0.047 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*sin(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 \sin {\left (x \right )}}{4} - \frac {\sin {\left (3 x \right )}}{4} + 5 \cos {\left (x \right )} \]