11.8.3 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 : Tuesday, September 30, 2025 at 06:38:51 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*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 34

ode=D[y[t],t]==2/(1-t^2)*y[t]+3; 
ic=y[1/2]==1; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 58

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - 3 - 2*y(t)/(1 - t**2),0) 
ics = {y(1/2): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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