74.12.48 problem 56

Internal problem ID [16355]
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 : 56
Date solved : Tuesday, January 28, 2025 at 09:06:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=t \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

dsolve(t^2*diff(y(t),t$2)+t*diff(y(t),t)+4*y(t)=t,y(t), singsol=all)
 

\[ y = \sin \left (2 \ln \left (t \right )\right ) c_{2} +\cos \left (2 \ln \left (t \right )\right ) c_{1} +\frac {t}{5} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 68

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

\[ y(t)\to \cos (2 \log (t)) \int _1^t-\frac {1}{2} \sin (2 \log (K[1]))dK[1]+\sin (2 \log (t)) \int _1^t\frac {1}{2} \cos (2 \log (K[2]))dK[2]+c_1 \cos (2 \log (t))+c_2 \sin (2 \log (t)) \]