4.16.9 \(y'(x)^2=y(x)^2+1\)

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 = 0.0182653 (sec), leaf count = 23

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

Maple
cpu = 0.037 (sec), leaf count = 31

\[ \left \{ 1+ \left (y \relax (x ) \right ) ^{2}=0,x-{\it Arcsinh} \left (y \relax (x ) \right ) -{\it \_C1}=0,x+{\it Arcsinh} \left (y \relax (x ) \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1+y(x)^2 = 0, x-arcsinh(y(x))-_C1 = 0, x+arcsinh(y(x))-_C1 = 0