38.4.1 problem 1

Internal problem ID [6487]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:07:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(2*diff(y(x),x$2)-7*diff(y(x),x)-4*y(x)=exp(3*x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{4 x}+{\mathrm e}^{-\frac {x}{2}} c_1 -\frac {{\mathrm e}^{3 x}}{7} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 33

DSolve[2*D[y[x],{x,2}]-7*D[y[x],x]-4*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{3 x}}{7}+c_1 e^{-x/2}+c_2 e^{4 x} \]