Internal problem ID [13823]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {25-y^{2}}=0} \] With initial conditions \begin {align*} [y \left (3\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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: 0.043 (sec). Leaf size: 23
DSolve[{y'[t]==Sqrt[25-y[t]^2],{y[3]==-6}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 5 \cos \left (-2 i \text {arctanh}\left (\sqrt {11}\right )-t+3\right ) \]