38.4.14 problem 15

Internal problem ID [6500]
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 : Monday, January 27, 2025 at 02:08:59 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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 30

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

\[ y(x)\to -e^{-2 x} \left (e^x-1\right )+\frac {3 \sin (x)}{10}-\frac {9 \cos (x)}{10} \]