Internal problem ID [14593]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-25 y=\frac {1}{1-{\mathrm e}^{5 t}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 77
dsolve(diff(y(t),t$2)-25*y(t)=(1-exp(5*t))^(-1),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (\ln \left ({\mathrm e}^{4 t}+{\mathrm e}^{3 t}+{\mathrm e}^{2 t}+{\mathrm e}^{t}+1\right ) {\mathrm e}^{10 t}+\ln \left ({\mathrm e}^{t}-1\right ) {\mathrm e}^{10 t}-5 \ln \left ({\mathrm e}^{t}\right ) {\mathrm e}^{10 t}-50 c_{2} {\mathrm e}^{10 t}+{\mathrm e}^{5 t}-\ln \left (1-{\mathrm e}^{5 t}\right )-50 c_{1} \right ) {\mathrm e}^{-5 t}}{50} \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 110
DSolve[y''[t]-25*y[t]==(1-Exp[5*t])^(-1),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{50} e^{-5 t} \left (-e^{5 t}+5 e^{10 t} \log \left (e^t\right )-\left (e^{10 t}-1\right ) \log \left (e^t-1\right )-e^{10 t} \log \left (e^t+e^{2 t}+e^{3 t}+e^{4 t}+1\right )+\log \left (e^t+e^{2 t}+e^{3 t}+e^{4 t}+1\right )+50 c_1 e^{10 t}+50 c_2\right ) \]