Internal problem ID [13833]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } t +y=t \sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (\pi \right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([t*diff(y(t),t)+y(t)=t*sin(t),y(Pi) = 1],y(t), singsol=all)
\[ y = \frac {\sin \left (t \right )-\cos \left (t \right ) t}{t} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 16
DSolve[{t*y'[t]+y[t]==t*Sin[t],{y[Pi]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sin (t)}{t}-\cos (t) \]