74.12.47 problem 55

Internal problem ID [16354]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 55
Date solved : Tuesday, January 28, 2025 at 09:06:39 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=\ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=ln(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 22

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==Log[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {-2 t+(t+c_2) \log (t)+c_1}{t} \]