Internal problem ID [4684]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2} \left (-x^{2}+1\right )=-1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 33
dsolve(diff(y(x),x)^2*(1-x^2)+1=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y \left (x \right ) &= -\ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 89
DSolve[y'[x]^2*(1-x^2)+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) \\ y(x)\to \frac {1}{2} \left (-\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) \\ \end{align*}