4.16.10 \(y'(x)^2=1-y(x)^2\)

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

[_quadrature]

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

Mathematica
cpu = 0.0206683 (sec), leaf count = 23

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

Maple
cpu = 0.036 (sec), leaf count = 31

\[ \left \{ \left (y \relax (x ) \right ) ^{2}-1=0,x-\arcsin \left (y \relax (x ) \right ) -{\it \_C1}=0,x+\arcsin \left (y \relax (x ) \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x]^2 == 1 - y[x]^2,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)^2 = 1-y(x)^2, y(x),'implicit')

Maple raw output

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