Internal problem ID [14706]
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: 31.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(t^2*ln(t)*diff(y(t),t$3)-t*diff(y(t),t$2)+diff(y(t),t)=1,y(t), singsol=all)
\[ y \left (t \right ) = \frac {c_{2} t^{2}}{2}-\ln \left (t \right ) c_{1} t +t +c_{3} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 25
DSolve[t^2*Log[t]*y'''[t]-t*y''[t]+y'[t]==1,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {c_1 t^2}{2}+t-c_2 t \log (t)+c_3 \]