ODE
\[ y'(x)^2=y(x)^2+1 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.200266 (sec), leaf count = 23
\[\{\{y(x)\to -\sinh (x-c_1)\},\{y(x)\to \sinh (x+c_1)\}\}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 31
\[[y \left (x \right ) = -i, y \left (x \right ) = i, y \left (x \right ) = -\sinh \left (-x +\textit {\_C1} \right ), y \left (x \right ) = \sinh \left (-x +\textit {\_C1} \right )]\] Mathematica raw input
DSolve[y'[x]^2 == 1 + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -Sinh[x - C[1]]}, {y[x] -> Sinh[x + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^2 = 1+y(x)^2, y(x))
Maple raw output
[y(x) = -I, y(x) = I, y(x) = -sinh(-x+_C1), y(x) = sinh(-x+_C1)]