Internal problem ID [472]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y+t y^{\prime }-\frac {\sin \relax (t )}{t}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (-\frac {\pi }{2}\right ) = a\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([2*y(t)+t*diff(y(t),t) = sin(t)/t,y(-1/2*Pi) = a],y(t), singsol=all)
\[ y \relax (t ) = \frac {-\cos \relax (t )+\frac {a \,\pi ^{2}}{4}}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 22
DSolve[{2*y[t]+t*y'[t] == Sin[t]/t,y[-Pi/2]==a},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\pi ^2 a-4 \cos (t)}{4 t^2} \\ \end{align*}