4.14 problem 15

Internal problem ID [4649]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-3 \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = -{\frac {9}{10}}, y^{\prime }\relax (0) = -{\frac {7}{10}}\right ] \end {align*}

Solution by Maple

Time used: 0.031 (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)
 

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

Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 29

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

\begin{align*} y(x)\to e^{-2 x}+\frac {3 \sin (x)}{10}-\frac {9 \cos (x)}{10}+\sinh (x)-\cosh (x) \\ \end{align*}