78.12.23 problem 2 (e)

Internal problem ID [18310]
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 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 2 (e)
Date solved : Tuesday, January 28, 2025 at 11:45:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2+3 \sqrt {2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 24

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+2*y(x)=0,y(0) = -1, D(y)(0) = 2+3*2^(1/2)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 30

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

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