Internal problem ID [14693]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }=-\frac {1}{t^{2}}-\frac {2}{t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(t),t$3)-2*diff(y(t),t$2)=-1/t^2-2/t,y(t), singsol=all)
\[ y \left (t \right ) = \frac {c_{1} {\mathrm e}^{2 t}}{4}+t \ln \left (2\right )+t \ln \left (t \right )+\left (c_{2} -1\right ) t +c_{3} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 29
DSolve[y'''[t]-2*y''[t]==-1/t^2-2/t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t \log (t)+\frac {1}{4} c_1 e^{2 t}+(-1+c_3) t+c_2 \]