Internal problem ID [14266]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 38 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}=\frac {1}{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(t),t$2)-1/t*diff(y(t),t)+1/t^2*y(t)=1/t,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{2} +c_{1} \ln \left (t \right )+\frac {\ln \left (t \right )^{2}}{2}\right ) t \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 25
DSolve[y''[t]-1/t*y'[t]+1/t^2*y[t]==1/t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} t \left (\log ^2(t)+2 c_2 \log (t)+2 c_1\right ) \]