28.9 problem 807

Internal problem ID [3538]

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]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 y^{\prime } \cosh \relax (x )+1=0} \end {gather*}

Solution by Maple

Time used: 0.203 (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 \relax (x ) = -{\mathrm e}^{-x}+c_{1} \\ y \relax (x ) = {\mathrm e}^{x}+c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

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 e^x+c_1 \\ \end{align*}