Internal problem ID [1975]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-3, page 12
Problem number: 1.2-3 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y}{-t^{2}+1}-3=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {1}{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 34
dsolve([diff(y(t),t)=2/(1-t^2)*y(t)+3,y(1/2) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (t +1\right ) \left (18 t -36 \ln \left (t +1\right )-11+36 \ln \relax (3)-36 \ln \relax (2)\right )}{6 t -6} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 34
DSolve[{y'[t]==2/(1-t^2)*y[t]+3,y[1/2]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {(t+1) \left (18 t-36 \log (t+1)-11+36 \log \left (\frac {3}{2}\right )\right )}{6 (t-1)} \\ \end{align*}