Internal problem ID [14109]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+45 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+45*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{1} \sin \left (6 x \right )+c_{2} \cos \left (6 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 26
DSolve[y''[x]-6*y'[x]+45*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} (c_2 \cos (6 x)+c_1 \sin (6 x)) \]