13.3.6 problem 6

Internal problem ID [2323]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:45:42 AM
CAS classification : [_separable]

\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 16

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

\[ y = \sqrt {2 \,{\mathrm e}^{-\frac {t^{3}}{3}}-1} \]

✓ Solution by Mathematica

Time used: 3.678 (sec). Leaf size: 43

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

\begin{align*} y(t)\to \sqrt {2 e^{-\frac {t^3}{3}}-1} \\ y(t)\to \sqrt {2 e^{-\frac {t^3}{3}}-1} \\ \end{align*}