76.13.31 problem 31

Internal problem ID [17613]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 10:45:26 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 16

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

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