35.6.29 problem 35

Internal problem ID [6179]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 35
Date solved : Monday, January 27, 2025 at 01:46:48 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 38

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

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