38.4.5 problem 5

Internal problem ID [6491]
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 : 5
Date solved : Monday, January 27, 2025 at 02:07:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 \cosh \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\[ y = \frac {\left (9 \,{\mathrm e}^{4 x}+36 \,{\mathrm e}^{3 x} c_2 +36 c_1 -12 x -7\right ) {\mathrm e}^{-2 x}}{36} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{36} e^{-2 x} \left (-12 x+9 e^{4 x}+36 c_2 e^{3 x}-4+36 c_1\right ) \]