74.3.18 problem 14 (c)

Internal problem ID [15878]
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 (c)
Date solved : Tuesday, January 28, 2025 at 08:16:16 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (3\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.181 (sec). Leaf size: 14

dsolve([diff(y(t),t)=sqrt(25-y(t)^2),y(3) = -6],y(t), singsol=all)
 

\[ y = 5 \sin \left (t -3-\arcsin \left (\frac {6}{5}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 49

DSolve[{D[y[t],t]==Sqrt[25-y[t]^2],{y[3]==-6}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {5 \tan \left (-i \text {arctanh}\left (\frac {6}{\sqrt {11}}\right )-t+3\right )}{\sqrt {\sec ^2\left (-i \text {arctanh}\left (\frac {6}{\sqrt {11}}\right )-t+3\right )}} \]