23.3.20 problem 9(a)

Internal problem ID [4161]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 9(a)
Date solved : Monday, January 27, 2025 at 08:41:01 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 )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 14

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

\[ y(x)\to e^x \left (e^x-1\right ) \]