13.3.8 problem 8

Internal problem ID [2325]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:45:48 AM
CAS classification : [_separable]

\begin{align*} \sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 16

dsolve([(t^2+1)^(1/2)*diff(y(t),t) = t*y(t)^3/(t^2+1)^(1/2),y(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 19

DSolve[{(t^2+1)^(1/2)*D[y[t],t] == t*y[t]^3/(t^2+1)^(1/2),y[0]==1},y[t],t,IncludeSingularSolutions -> True]
 

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