14.1.15 problem 15

Internal problem ID [2486]
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 : 15
Date solved : Sunday, March 30, 2025 at 12:03:03 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=(t^2+1)*diff(y(t),t)+t*y(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: 0.078 (sec). Leaf size: 36

ode=(1+t^2)*D[y[t],t]+t*y[t]==(1+t^2)^(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: 0.841 (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)
 

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