Internal problem ID [14594]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=2 \sinh \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)-y(t)=2*sinh(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (2 t +4 c_{2} \right ) {\mathrm e}^{-t}}{4}+\frac {\left (t +2 c_{1} -\frac {1}{2}\right ) {\mathrm e}^{t}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 38
DSolve[y''[t]-y[t]==2*Sinh[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-t} \left (2 t+e^{2 t} (2 t-1+4 c_1)+1+4 c_2\right ) \]