32.4.17 problem 18

Internal problem ID [7790]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 05:05:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }&=3 \sin \left (x \right )-4 y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (\frac {\pi }{2}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x) = 3*sin(x)-4*y(x); 
ic:=[y(0) = 0, D(y)(1/2*Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\sin \left (2 x \right )}{2}+\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 13

ode=D[y[x],{x,2}]==3*Sin[x]-4*y[x]; 
ic={y[0]==0,Derivative[1][y][Pi/2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -(\sin (x) (\cos (x)-1)) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 3*sin(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, pi/2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sin {\left (x \right )} - \frac {\sin {\left (2 x \right )}}{2} \]