34.1.4 problem 4

Internal problem ID [6028]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 1, Nature and meaning of a differential equation between two variables. page 12
Problem number : 4
Date solved : Monday, January 27, 2025 at 01:33:39 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2} \left (-x^{2}+1\right )+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 33

dsolve(diff(y(x),x)^2*(1-x^2)+1=0,y(x), singsol=all)
 

\begin{align*} y &= \ln \left (x +\sqrt {x^{2}-1}\right )+c_1 \\ y &= -\ln \left (x +\sqrt {x^{2}-1}\right )+c_1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 41

DSolve[D[y[x],x]^2*(1-x^2)+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\log \left (\sqrt {x^2-1}+x\right )+c_1 \\ y(x)\to \log \left (\sqrt {x^2-1}+x\right )+c_1 \\ \end{align*}