78.10.6 problem 6 (a)

Internal problem ID [18267]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:44:51 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+diff(y(x),x)-2*y(x)=0,y(0) = 8, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = \left (6 \,{\mathrm e}^{3 x}+2\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}] +D[y[x],x]-2*y[x]==0,{y[0]==8,Derivative[1][y][0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{-2 x}+6 e^x \]