74.18.46 problem 53

Internal problem ID [16603]
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
Date solved : Tuesday, January 28, 2025 at 09:12:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime } t +t^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.061 (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)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 39

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

\[ y(t)\to \frac {1}{2} e^{\frac {1}{2} t (t-2 i)} \left (2 c_1-i c_2 e^{2 i t}\right ) \]