Internal problem ID [1746]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 18
dsolve(diff(y(t),t$2)-4*t*diff(y(t),t)+(4*t^2-2)*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{t^{2}} c_{1}+c_{2} t \,{\mathrm e}^{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 18
DSolve[y''[t]-4*t*y'[t]+(4*t^2-2)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{t^2} (c_2 t+c_1) \\ \end{align*}