Internal problem ID [465]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y+t y^{\prime }-\sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([2*y(t)+t*diff(y(t),t) = sin(t),y(1/2*Pi) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\sin \relax (t )-\cos \relax (t ) t +\frac {\pi ^{2}}{4}-1}{t^{2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 26
DSolve[{2*y[t]+t*y'[t] == Sin[t],y[Pi/2]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4 \sin (t)-4 t \cos (t)+\pi ^2-4}{4 t^2} \\ \end{align*}