4.17.11 \(y'(x)^2-2 \cosh (x) y'(x)+1=0\)

ODE
\[ y'(x)^2-2 \cosh (x) y'(x)+1=0 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.0167839 (sec), leaf count = 25

\[\left \{\left \{y(x)\to c_1+\sinh (x)-\cosh (x)\right \},\left \{y(x)\to c_1+\sinh (x)+\cosh (x)\right \}\right \}\]

Maple
cpu = 0.035 (sec), leaf count = 19

\[ \left \{ y \relax (x ) =- \left ({{\rm e}^{x}} \right ) ^{-1}+{\it \_C1},y \relax (x ) ={{\rm e}^{x}}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[1 - 2*Cosh[x]*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1] - Cosh[x] + Sinh[x]}, {y[x] -> C[1] + Cosh[x] + Sinh[x]}}

Maple raw input

dsolve(diff(y(x),x)^2-2*diff(y(x),x)*cosh(x)+1 = 0, y(x),'implicit')

Maple raw output

y(x) = -1/exp(x)+_C1, y(x) = exp(x)+_C1