80.6.8 problem 9 (b)

Internal problem ID [18572]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 9 (b)
Date solved : Tuesday, January 28, 2025 at 12:00:41 PM
CAS classification : [_separable]

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

dsolve(sqrt(1-u^2)*diff(v(u),u)=2*u*sqrt(1-v(u)^2),v(u), singsol=all)
 

\[ v = \sin \left (\frac {2 c_{1} \sqrt {-u^{2}+1}+2 u^{2}-2}{\sqrt {-u^{2}+1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.257 (sec). Leaf size: 44

DSolve[Sqrt[1-u^2]*D[v[u],u]==2*u*Sqrt[1-v[u]^2],v[u],u,IncludeSingularSolutions -> True]
 

\begin{align*} v(u)\to -\sin \left (2 \sqrt {1-u^2}-c_1\right ) \\ v(u)\to -1 \\ v(u)\to 1 \\ v(u)\to \text {Interval}[\{-1,1\}] \\ \end{align*}