8.11.27 problem 50

Internal problem ID [895]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 50
Date solved : Monday, January 27, 2025 at 03:16:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 38

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

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