Internal problem ID [1725]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(t^2*diff(y(t),t$2)+alpha*t*diff(y(t),t)+beta*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t^{-\frac {\alpha }{2}+\frac {1}{2}+\frac {\sqrt {\alpha ^{2}-2 \alpha -4 \beta +1}}{2}}+c_{2} t^{-\frac {\alpha }{2}+\frac {1}{2}-\frac {\sqrt {\alpha ^{2}-2 \alpha -4 \beta +1}}{2}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 53
DSolve[t^2*y''[t]+\[Alpha]*t*y'[t]+\[Beta]*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^{\frac {1}{2} \left (-\sqrt {(\alpha -1)^2-4 \beta }-\alpha +1\right )} \left (c_2 t^{\sqrt {(\alpha -1)^2-4 \beta }}+c_1\right ) \\ \end{align*}