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 : Monday, January 27, 2025 at 05:54:04 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 36

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

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