76.13.37 problem 37

Internal problem ID [17619]
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 : 37
Date solved : Tuesday, January 28, 2025 at 10:45:41 AM
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 (-1\right )&=2\\ y^{\prime }\left (-1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 16

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

\[ y = {\mathrm e}^{-2 x -2} \left (5 x +7\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to e^{-2 (x+1)} (5 x+7) \]