Internal problem ID [14631]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t y^{\prime \prime }+2 y^{\prime }+t y=-t} \] With initial conditions \begin {align*} \left [y \left (\pi \right ) = -1, y^{\prime }\left (\pi \right ) = -\frac {1}{\pi }\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 12
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)
\[ y \left (t \right ) = \frac {-t +\sin \left (t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 36
DSolve[{t*y''[t]+2*y'[t]+t*y[t]==-t,{y[Pi]==-1,y'[Pi]==-1/Pi}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {i \left (2 i t+e^{-i t}-e^{i t}\right )}{2 t} \]