64.10.31 problem 31

Internal problem ID [13437]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 05:42:29 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 (0\right )&=3\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=0,y(0) = 3, D(y)(0) = 7],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (3+13 x \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==0,{y[0]==3,Derivative[1][y][0] ==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} (13 x+3) \]