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 = 0.171181 (sec), leaf count = 25
\[\{\{y(x)\to \sinh (x)-\cosh (x)+c_1\},\{y(x)\to \sinh (x)+\cosh (x)+c_1\}\}\]
Maple ✓
cpu = 0.077 (sec), leaf count = 19
\[[y \left (x \right ) = -{\mathrm e}^{-x}+\textit {\_C1}, y \left (x \right ) = {\mathrm e}^{x}+\textit {\_C1}]\] 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))
Maple raw output
[y(x) = -1/exp(x)+_C1, y(x) = exp(x)+_C1]