12.8.1 problem 1

Internal problem ID [1737]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 1
Date solved : Monday, January 27, 2025 at 05:33:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 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: 0.011 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)-7*diff(y(x),x)+10*y(x)=0,y(0) = -1, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x}-2 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-7*D[y[x],x]+10*y[x]==0,{y[0]==-1,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

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