Internal problem ID [455]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {4 y t +\left (t^{2}+1\right ) y^{\prime }-\frac {1}{\left (t^{2}+1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve(4*t*y(t)+(t^2+1)*diff(y(t),t) = 1/(t^2+1)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {\arctan \relax (t )+c_{1}}{\left (t^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 18
DSolve[4*t*y[t]+(t^2+1)*y'[t] == 1/(t^2+1)^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\text {ArcTan}(t)+c_1}{\left (t^2+1\right )^2} \\ \end{align*}