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 : Monday, January 27, 2025 at 05:45:22 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: 0.001 (sec). Leaf size: 30

dsolve(t*y(t)+(t^2+1)*diff(y(t),t) = (t^2+1)^(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: 0.068 (sec). Leaf size: 36

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

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