32.7.23 problem Exercise 20.24, page 220

Internal problem ID [5938]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.24, page 220
Date solved : Monday, January 27, 2025 at 01:27:46 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}} \left (c_{1} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{2} \cos \left (\frac {\sqrt {3}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 42

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

\[ y(x)\to e^{x/2} \left (c_1 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]