Internal problem ID [14469]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }+a t y^{\prime }+b y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve(t^2*diff(y(t),t$2)+a*t*diff(y(t),t)+b*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \sqrt {t}\, t^{-\frac {a}{2}} \left (t^{\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{1} +t^{-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 57
DSolve[t^2*y''[t]+a*t*y'[t]+b*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}-a+1\right )} \left (c_2 t^{\sqrt {a^2-2 a-4 b+1}}+c_1\right ) \]