Internal problem ID [462]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 y+t y^{\prime }-t^{2}+t -1=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([2*y(t)+t*diff(y(t),t) = t^2-t+1,y(1) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2}}{4}-\frac {t}{3}+\frac {1}{2}+\frac {1}{12 t^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 22
DSolve[{2*y[t]+t*y'[t] == t^2-t+1,y[1]==1/2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{12} \left (3 t^2+\frac {1}{t^2}-4 t+6\right ) \\ \end{align*}