76.13.30 problem 30

Internal problem ID [17612]
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 : 30
Date solved : Tuesday, January 28, 2025 at 10:45:25 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 17

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

\[ y = 3 \,{\mathrm e}^{-x}-{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

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

\[ y(x)\to e^{-2 x} \left (3 e^x-1\right ) \]