74.12.55 problem 62 (a)

Internal problem ID [16362]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 62 (a)
Date solved : Tuesday, January 28, 2025 at 09:06:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=-1\\ y^{\prime }\left (\pi \right )&=-\frac {1}{\pi } \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 14

dsolve([t*diff(y(t),t$2)+2*diff(y(t),t)+t*y(t)=-t,y(Pi) = -1, D(y)(Pi) = -1/Pi],y(t), singsol=all)
 

\[ y = \frac {-t +\sin \left (t \right )}{t} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 36

DSolve[{t*D[y[t],{t,2}]+2*D[y[t],t]+t*y[t]==-t,{y[Pi]==-1,Derivative[1][y][Pi]==-1/Pi}},y[t],t,IncludeSingularSolutions -> True]
 

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