64.10.36 problem 36

Internal problem ID [13442]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 05:42:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=0,y(0) = 2, D(y)(0) = 6],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 23

DSolve[{D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==0,{y[0]==2,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{-x} (2 \sin (2 x)+\cos (2 x)) \]