32.7.31 problem Exercise 20, problem 32, page 220

Internal problem ID [5946]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 32, page 220
Date solved : Monday, January 27, 2025 at 01:28:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 16

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

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