82.18.12 problem Ex. 13

Internal problem ID [18834]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 13
Date solved : Tuesday, January 28, 2025 at 12:24:11 PM
CAS classification : [_quadrature]

\begin{align*} y^{2} \left (1-{y^{\prime }}^{2}\right )&=b \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 51

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

\begin{align*} y \left (x \right ) &= \sqrt {b} \\ y \left (x \right ) &= -\sqrt {b} \\ y \left (x \right ) &= \sqrt {c_{1}^{2}-2 c_{1} x +x^{2}+b} \\ y \left (x \right ) &= -\sqrt {c_{1}^{2}-2 c_{1} x +x^{2}+b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 93

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

\begin{align*} y(x)\to -\sqrt {b+(x-c_1){}^2} \\ y(x)\to \sqrt {b+(x-c_1){}^2} \\ y(x)\to -\sqrt {b+(x+c_1){}^2} \\ y(x)\to \sqrt {b+(x+c_1){}^2} \\ y(x)\to -\sqrt {b} \\ y(x)\to \sqrt {b} \\ \end{align*}