20.1.33 problem Problem 45

Internal problem ID [3590]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 45
Date solved : Monday, January 27, 2025 at 07:46:50 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \left ({\mathrm e}^{5 x} c_{2} +c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 19

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

\[ y(x)\to e^x (x-2)+c_2 x+c_1 \]