Internal problem ID [3996]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 755.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-y^{2}=1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve(diff(y(x),x)^2 = 1+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i y \left (x \right ) = i y \left (x \right ) = -\sinh \left (c_{1} -x \right ) y \left (x \right ) = \sinh \left (c_{1} -x \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.284 (sec). Leaf size: 69
DSolve[(y'[x])^2==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{-x+c_1}-e^{x-c_1}\right ) y(x)\to \frac {1}{2} \left (e^{x+c_1}-e^{-x-c_1}\right ) y(x)\to -i y(x)\to i \end{align*}