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