74.5.37 problem 38 (c)

Internal problem ID [16001]
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)
Date solved : Tuesday, January 28, 2025 at 08:26:11 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \left (c_{2} +\frac {\ln \left (t \right )^{2}}{2}+c_{1} \ln \left (t \right )\right ) t \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

DSolve[D[y[t],{t,2}]-1/t*D[y[t],t]+1/t^2*y[t]==1/t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} t \left (\log ^2(t)+2 c_2 \log (t)+2 c_1\right ) \]