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]]
\[ \boxed {t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve(t^2*diff(y(t),t$2)+alpha*t*diff(y(t),t)+beta*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \sqrt {t}\, t^{-\frac {\alpha }{2}} \left (t^{\frac {\sqrt {\alpha ^{2}-2 \alpha -4 \beta +1}}{2}} c_{1} +t^{-\frac {\sqrt {\alpha ^{2}-2 \alpha -4 \beta +1}}{2}} c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 57
DSolve[t^2*y''[t]+\[Alpha]*t*y'[t]+\[Beta]*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t^{\frac {1}{2} \left (-\sqrt {\alpha ^2-2 \alpha -4 \beta +1}-\alpha +1\right )} \left (c_2 t^{\sqrt {\alpha ^2-2 \alpha -4 \beta +1}}+c_1\right ) \]