78.10.7 problem 6 (c)

Internal problem ID [18268]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 6 (c)
Date solved : Tuesday, January 28, 2025 at 11:44:53 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 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: 0.010 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=0,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = -3 \,{\mathrm e}^{-3 x}+4 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}] +5*D[y[x],x]+6*y[x]==0,{y[0]==1,Derivative[1][y][0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (4 e^x-3\right ) \]