49.4.6 problem 1(f)

Internal problem ID [7617]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:07:42 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \]