59.1.613 problem 629

Internal problem ID [9785]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 629
Date solved : Monday, January 27, 2025 at 06:14:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 18

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

\[ y(t)\to e^{t^2} (c_2 t+c_1) \]