Internal problem ID [14873]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 53.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime } t +t^{2} y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 20
dsolve(diff(y(t),t$2)-2*t*diff(y(t),t)+t^2*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {t^{2}}{2}} \left (\sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 39
DSolve[y''[t]-2*t*y'[t]+t^2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{\frac {1}{2} t (t-2 i)} \left (2 c_1-i c_2 e^{2 i t}\right ) \]