Internal problem ID [14259]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } t +y=\cos \left (t \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = \frac {4}{\pi }\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([t*diff(y(t),t)+y(t)=cos(t),y(1/2*Pi) = 4/Pi],y(t), singsol=all)
\[ y \left (t \right ) = \frac {1+\sin \left (t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 13
DSolve[{t*y'[t]+y[t]==Cos[t],{y[Pi/2]==4/Pi}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sin (t)+1}{t} \]