Internal problem ID [14623]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }+y^{\prime } t +4 y=t} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \sin \left (2 \ln \left (t \right )\right ) c_{2} +\cos \left (2 \ln \left (t \right )\right ) c_{1} +\frac {t}{5} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 27
DSolve[t^2*y''[t]+t*y'[t]+4*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t}{5}+c_1 \cos (2 \log (t))+c_2 \sin (2 \log (t)) \]