76.3.16 problem 16

Internal problem ID [17387]
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 : 16
Date solved : Tuesday, January 28, 2025 at 10:04:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 t y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.775 (sec). Leaf size: 16

dsolve([diff(y(t),t)=2*t*y(t)^2,y(0) = y__0],y(t), singsol=all)
 

\[ y = -\frac {y_{0}}{t^{2} y_{0} -1} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 17

DSolve[{D[y[t],t]==2*t*y[t]^2,{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\text {y0}}{1-t^2 \text {y0}} \]