11.6.1 problem 1.2-1 (a)

Internal problem ID [3438]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (a)
Date solved : Tuesday, September 30, 2025 at 06:38:25 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (t^{2}+1\right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(t),t) = (t^2+1)*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 24

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

\begin{align*} y(t)&\to c_1 e^{\frac {t^3}{3}+t}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} e^{t \left (\frac {t^{2}}{3} + 1\right )} \]