Internal problem ID [6344]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 53.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {t y^{\prime \prime }-y^{\prime }+4 t^{3} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(t*diff(y(t),t$2)-diff(y(t),t)+4*t^3*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \sin \left (t^{2}\right )+c_{2} \cos \left (t^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 20
DSolve[t*y''[t]-y'[t]+4*t^3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \cos \left (t^2\right )+c_2 \sin \left (t^2\right ) \\ \end{align*}