38.3.1 problem 1

Internal problem ID [6479]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:07:23 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=8 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=8,y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{2 x} c_1 -4 \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-D[y[x],x]-2*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-x}+c_2 e^{2 x}-4 \]