8.11.8 problem 8

Internal problem ID [876]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 8
Date solved : Monday, January 27, 2025 at 03:12:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-4*y(x)=cosh(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-4 x +32 c_1 -2\right ) {\mathrm e}^{-2 x}}{32}+\frac {\left (x +8 c_2 -\frac {1}{4}\right ) {\mathrm e}^{2 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{32} e^{-2 x} \left (-4 x+e^{4 x} (4 x-1+32 c_1)-1+32 c_2\right ) \]