64.10.35 problem 35

Internal problem ID [13441]
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 : 35
Date solved : Tuesday, January 28, 2025 at 05:42:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 22

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+13*y(x)=0,y(0) = 3, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \left (4 \sin \left (2 x \right )+3 \cos \left (2 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+13*y[x]==0,{y[0]==3,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} (4 \sin (2 x)+3 \cos (2 x)) \]