Internal problem ID [14707]
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: 32.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime }=-t -2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((t^2+t)*diff(y(t),t$3)+(2-t^2)*diff(y(t),t$2)-(t+2)*diff(y(t),t)=-2-t,y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \ln \left (t \right )+{\mathrm e}^{t} c_{1} +t +c_{3} \]
✓ Solution by Mathematica
Time used: 0.479 (sec). Leaf size: 38
DSolve[(t^2+t)*y'''[t]+(2-t^2)*y''[t]-(t+2)*y'[t]==-2-t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t+\log (t)+\sqrt {2} c_2 e^{t+\frac {1}{2}}+\frac {c_1 \log (t)}{\sqrt {2 e}}+c_3 \]