8.7.12 problem 12

Internal problem ID [818]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 12
Date solved : Wednesday, February 05, 2025 at 04:34:05 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 )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

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

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