Internal problem ID [5949]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (c_{1} \sin \left (x \right )+\cos \left (x \right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 22
DSolve[y''[x]-4*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \]