35.5.5 problem 5

Internal problem ID [6139]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 5
Date solved : Monday, January 27, 2025 at 01:38:11 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_1 \sin \left (\sqrt {5}\, x \right )+c_2 \cos \left (\sqrt {5}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\sqrt {5} x\right )+c_1 \sin \left (\sqrt {5} x\right )\right ) \]