76.3.17 problem 17

Internal problem ID [17388]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 10:04:11 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{3}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.108 (sec). Leaf size: 16

dsolve([diff(y(t),t)+y(t)^3=0,y(0) = y__0],y(t), singsol=all)
 

\[ y = \frac {y_{0}}{\sqrt {2 t \,y_{0}^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 33

DSolve[{D[y[t],t]+y[t]^3==0,{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {1}{\sqrt {2 t+\frac {1}{\text {y0}^2}}} \\ y(t)\to \frac {1}{\sqrt {2 t+\frac {1}{\text {y0}^2}}} \\ \end{align*}