32.4.14 problem 15

Internal problem ID [7787]
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 : 15
Date solved : Tuesday, September 30, 2025 at 05:05:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {9}{10}} \\ y^{\prime }\left (0\right )&=-{\frac {7}{10}} \\ \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = 3*sin(x); 
ic:=[y(0) = -9/10, D(y)(0) = -7/10]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x}-\frac {9 \cos \left (x \right )}{10}+\frac {3 \sin \left (x \right )}{10}-{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 30

ode=D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==3*Sin[x]; 
ic={y[0]==-9/10,Derivative[1][y][0] ==-7/10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -e^{-2 x} \left (e^x-1\right )+\frac {3 \sin (x)}{10}-\frac {9 \cos (x)}{10} \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 3*sin(x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -9/10, Subs(Derivative(y(x), x), x, 0): -7/10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 \sin {\left (x \right )}}{10} - \frac {9 \cos {\left (x \right )}}{10} - e^{- x} + e^{- 2 x} \]