76.3.14 problem 14

Internal problem ID [17385]
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 : 14
Date solved : Tuesday, January 28, 2025 at 10:03:59 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime }&=-\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 3.907 (sec). Leaf size: 17

dsolve([diff(y(t),t)=(-t+(t^2+4*y(t))^(1/2))/2,y(2) = -1],y(t), singsol=all)
 

\begin{align*} y &= 1-t \\ y &= -\frac {t^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.791 (sec). Leaf size: 10

DSolve[{D[y[t],t]==(-t+(t^2+4*y[t])^(1/2))/2,{y[2]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 1-t \]