13.2.15 problem 16

Internal problem ID [2313]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 16
Date solved : Saturday, March 29, 2025 at 11:53:49 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 15

ode:=4*t*y(t)+(t^2+1)*diff(y(t),t) = t; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {1}{4}-\frac {1}{4 \left (t^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 24

ode=4*t*y[t]+(t^2+1)*D[y[t],t]== t; 
ic=y[0]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^2 \left (t^2+2\right )}{4 \left (t^2+1\right )^2} \]

✓ Sympy. Time used: 0.336 (sec). Leaf size: 19

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(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{4} - \frac {1}{4 \left (t^{4} + 2 t^{2} + 1\right )} \]