Internal problem ID [14592]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y=\frac {1}{1+{\mathrm e}^{3 t}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 69
dsolve(diff(y(t),t$2)-9*y(t)=(1+exp(3*t))^(-1),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-3 t} \left (\ln \left ({\mathrm e}^{2 t}-{\mathrm e}^{t}+1\right ) {\mathrm e}^{6 t}-\ln \left (1+{\mathrm e}^{3 t}\right )+\ln \left (1+{\mathrm e}^{t}\right ) {\mathrm e}^{6 t}+\left (18 c_{1} -3 \ln \left ({\mathrm e}^{t}\right )\right ) {\mathrm e}^{6 t}+18 c_{2} -{\mathrm e}^{3 t}\right )}{18} \]
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 94
DSolve[y''[t]-9*y[t]==(1+Exp[3*t])^(-1),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{18} e^{-3 t} \left (-e^{3 t}-3 e^{6 t} \log \left (e^t\right )+\left (e^{6 t}-1\right ) \log \left (e^t+1\right )+e^{6 t} \log \left (-e^t+e^{2 t}+1\right )-\log \left (-e^t+e^{2 t}+1\right )+18 c_1 e^{6 t}+18 c_2\right ) \]