78.10.3 problem 3

Internal problem ID [18264]
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 : 3
Date solved : Tuesday, January 28, 2025 at 11:44:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 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: 15

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 16

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

\[ y(x)\to e^x \left (2 e^x-3\right ) \]