Internal problem ID [4046]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 807.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )=-1} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 19
dsolve(diff(y(x),x)^2-2*diff(y(x),x)*cosh(x)+1 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -{\mathrm e}^{-x}+c_{1} y \left (x \right ) = {\mathrm e}^{x}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 25
DSolve[(y'[x])^2-2 y'[x] Cosh[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sinh (x)-\cosh (x)+c_1 y(x)\to \sinh (x)+\cosh (x)+c_1 \end{align*}