Internal problem ID [13729]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(t^2*diff(y(t),t$2)+t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y = c_{1} \sin \left (\sqrt {2}\, \ln \left (t \right )\right )+c_{2} \cos \left (\sqrt {2}\, \ln \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 30
DSolve[t^2*y''[t]+t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 \cos \left (\sqrt {2} \log (t)\right )+c_2 \sin \left (\sqrt {2} \log (t)\right ) \]