38.3.8 problem 8

Internal problem ID [6486]
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 : 8
Date solved : Monday, January 27, 2025 at 02:07:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=8*exp(4*x),y(x), singsol=all)
 

\[ y = \frac {\left (8 x +c_1 -4\right ) {\mathrm e}^{4 x}}{2}+c_2 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==8*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

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