74.3.16 problem 14 (a)

Internal problem ID [15876]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 14 (a)
Date solved : Tuesday, January 28, 2025 at 08:11:28 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (-4\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.093 (sec). Leaf size: 12

dsolve([diff(y(t),t)=sqrt(25-y(t)^2),y(-4) = 3],y(t), singsol=all)
 

\[ y = 5 \sin \left (t +4+\arcsin \left (\frac {3}{5}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 29

DSolve[{D[y[t],t]==Sqrt[25-y[t]^2],{y[-4]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {5 \tan \left (\arctan \left (\frac {3}{4}\right )+t+4\right )}{\sqrt {\sec ^2\left (\arctan \left (\frac {3}{4}\right )+t+4\right )}} \]