74.2.8 problem 13

Internal problem ID [15849]
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 : 13
Date solved : Tuesday, January 28, 2025 at 08:09:36 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=2 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-7*diff(y(x),x)+12*y(x)=2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{4 x} c_{1} +\frac {1}{6} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-7*D[y[x],x]+12*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{3 x}+c_2 e^{4 x}+\frac {1}{6} \]