56.1.53 problem 53

Internal problem ID [8765]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 53
Date solved : Monday, January 27, 2025 at 04:48:32 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y = c_{1} \sin \left (t^{2}\right )+c_{2} \cos \left (t^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 20

DSolve[t*D[y[t],{t,2}]-D[y[t],t]+4*t^3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 \cos \left (t^2\right )+c_2 \sin \left (t^2\right ) \]