14.4.19 problem 19

Internal problem ID [2537]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:59:36 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 5

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

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 6

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

\[ y(t)\to 1 \]