8.1.16 problem 16

Internal problem ID [2487]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 05:36:51 AM
CAS classification : [_separable]

\begin{align*} \left (t^{2}+1\right ) y^{\prime }+4 t y&=t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{4}} \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 5

ode:=(t^2+1)*diff(y(t),t)+4*t*y(t) = t; 
ic:=[y(1) = 1/4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = {\frac {1}{4}} \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 8

ode=(1+t^2)*D[y[t],t]+4*t*y[t]==t; 
ic={y[1]==1/4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} \end{align*}

✓ Sympy. Time used: 0.220 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*t*y(t) - t + (t**2 + 1)*Derivative(y(t), t),0) 
ics = {y(1): 1/4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{4} \]