59.1.392 problem 404

Internal problem ID [9564]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 404
Date solved : Monday, January 27, 2025 at 06:04:09 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 42

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

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