17.8.3 problem 1.2-3 (c)

Internal problem ID [3455]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (c)
Date solved : Monday, January 27, 2025 at 07:37:18 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 34

dsolve([diff(y(t),t)=2/(1-t^2)*y(t)+3,y(1/2) = 1],y(t), singsol=all)
 

\[ y = \frac {\left (t +1\right ) \left (18 t -36 \ln \left (t +1\right )-11+36 \ln \left (3\right )-36 \ln \left (2\right )\right )}{-6+6 t} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 34

DSolve[{D[y[t],t]==2/(1-t^2)*y[t]+3,y[1/2]==1},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {(t+1) \left (18 t-36 \log (t+1)-11+36 \log \left (\frac {3}{2}\right )\right )}{6 (t-1)} \]