6.29 problem 35

Internal problem ID [4327]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-y-\sinh \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

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

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

Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 38

DSolve[y''[x]-y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} 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 ) \\ \end{align*}