Internal problem ID [1727]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-t y^{\prime }-2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.04 (sec). Leaf size: 28
dsolve([t^2*diff(y(t),t$2)-t*diff(y(t),t)-2*y(t)=0,y(1) = 0, D(y)(1) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\sqrt {3}\, \left (t^{1+\sqrt {3}}-t^{-\sqrt {3}+1}\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{t^2*y''[t]-t*y'[t]-2*y[t]==0,{y[1]==0,y'[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t^{1-\sqrt {3}} \left (t^{2 \sqrt {3}}-1\right )}{2 \sqrt {3}} \\ \end{align*}