74.12.49 problem 57

Internal problem ID [16356]
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 : 57
Date solved : Tuesday, January 28, 2025 at 09:06:46 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=2 \ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(t^2*diff(y(t),t$2)-4*t*diff(y(t),t)-6*y(t)=2*ln(t),y(t), singsol=all)
 

\[ y = t^{6} c_{2} -\frac {\ln \left (t \right )}{3}+\frac {5}{18}+\frac {c_{1}}{t} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 27

DSolve[t^2*D[y[t],{t,2}]-4*t*D[y[t],t]-6*y[t]==2*Log[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_2 t^6-\frac {\log (t)}{3}+\frac {c_1}{t}+\frac {5}{18} \]