7.11.7 problem 7

Internal problem ID [328]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:45:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 56

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

\[ y = \frac {\left (-2 \sinh \left (x \right )^{2} \cosh \left (x \right )-2 \sinh \left (x \right )^{3}+12 c_1 +\cosh \left (x \right )\right ) {\mathrm e}^{-2 x}}{12}+\left (\frac {\sinh \left (x \right )^{2} \cosh \left (x \right )}{6}-\frac {\sinh \left (x \right )^{3}}{6}+c_2 -\frac {\cosh \left (x \right )}{12}\right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{6} e^{-2 x} \left (e^x-e^{3 x}+6 c_1 e^{4 x}+6 c_2\right ) \]