13.2.14 problem 15

Internal problem ID [2312]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 15
Date solved : Saturday, March 29, 2025 at 11:53:46 PM
CAS classification : [_linear]

\begin{align*} t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=t*y(t)+(t^2+1)*diff(y(t),t) = (t^2+1)^(5/2); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {3 t^{5}+10 t^{3}+15 c_1 +15 t}{15 \sqrt {t^{2}+1}} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 36

ode=t*y[t]+(t^2+1)*D[y[t],t] == (t^2+1)^(5/2); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {3 t^5+10 t^3+15 t+15 c_1}{15 \sqrt {t^2+1}} \]

✓ Sympy. Time used: 0.862 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*y(t) - (t**2 + 1)**(5/2) + (t**2 + 1)*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1} + \frac {t^{5}}{5} + \frac {2 t^{3}}{3} + t}{\sqrt {t^{2} + 1}} \]