Internal problem ID [4835]
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]]
\[ \boxed {y^{\prime \prime }-y=\sinh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-y(x)=sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x +8 c_{1} \right ) {\mathrm e}^{-x}}{8}+\frac {\left (x +4 c_{2} -\frac {1}{2}\right ) {\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 38
DSolve[y''[x]-y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^{-x} \left (2 x+e^{2 x} (2 x-1+8 c_1)+1+8 c_2\right ) \]