59.1.211 problem 214

Internal problem ID [9383]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 214
Date solved : Monday, January 27, 2025 at 06:02:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 21

dsolve(t*diff(y(t),t$2)+(1-t^2)*diff(y(t),t)+4*t*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {\left (t^{4}-8 t^{2}+8\right ) \left (c_{1} +2 c_{2} \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.622 (sec). Leaf size: 65

DSolve[t*D[y[t],{t,2}]+(1-t^2)*D[y[t],t]+4*t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {e} \left (t^4-8 t^2+8\right ) \left (c_2 \int _1^t\frac {e^{\frac {K[1]^2}{2}-1}}{K[1] \left (K[1]^4-8 K[1]^2+8\right )^2}dK[1]+c_1\right ) \]