14.2.8 problem 8

Internal problem ID [2496]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:54:28 AM
CAS classification : [_separable]

\begin{align*} \sqrt {1+y^{2}}\, 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: 0.447 (sec). Leaf size: 62

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

\[ y = \operatorname {RootOf}\left (\sqrt {2}\, \textit {\_Z}^{2}+\operatorname {arctanh}\left (\frac {\sqrt {2}}{2}\right ) \textit {\_Z}^{2}-\operatorname {arctanh}\left (\frac {1}{\sqrt {\textit {\_Z}^{2}+1}}\right ) \textit {\_Z}^{2}-2 \sqrt {t^{2}+1}\, \textit {\_Z}^{2}+2 \textit {\_Z}^{2}-\sqrt {\textit {\_Z}^{2}+1}\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out