8.3.5 problem 5

Internal problem ID [681]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:57:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

dsolve(2*x^(1/2)*diff(y(x),x) = (1-y(x)^2)^(1/2),y(x), singsol=all)
 

\[ y = \sin \left (\sqrt {x}+\frac {c_1}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 32

DSolve[2*x^(1/2)*D[y[x],x] == (1-y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin \left (\sqrt {x}+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}