ODE
\[ \left (1-x^2\right ) y'(x)^2=1-y(x)^2 \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.269248 (sec), leaf count = 287
\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-c_1} \sqrt {2 x^2-2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \sqrt {2 x^2-2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {e^{-2 c_1} \left (2 x^2+2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2-2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}\right )}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {e^{-2 c_1} \left (2 x^2+2 \sqrt {x^2-1} x+e^{4 c_1} \left (2 x^2-2 \sqrt {x^2-1} x-1\right )-1+2 e^{2 c_1}\right )}\right \}\right \}\]
Maple ✗
cpu = 0. (sec), leaf count = 0 , exception
time expired
Mathematica raw input
DSolve[(1 - x^2)*y'[x]^2 == 1 - y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*Sqrt[-1 + 2*E^(2*C[1]) + 2*x^2 - 2*x*Sqrt[-1 + x^2] + E^(4*C[1])*(-1 + 2*x^2 + 2*x*Sqrt[-1 + x^2])]/E^C[1]}, {y[x] -> Sqrt[-1 + 2*E^(2*C[1]) + 2*x^2 - 2*x*Sqrt[-1 + x^2] + E^(4*C[1])*(-1 + 2*x^2 + 2*x*Sqrt[-1 + x^2])]/(2*E^C[1])}, {y[x] -> -1/2*Sqrt[(-1 + 2*E^(2*C[1]) + 2*x^2 + 2*x*Sqrt[-1 + x^2] + E^(4*C[1])*(-1 + 2*x^2 - 2*x*Sqrt[-1 + x^2]))/E^(2*C[1])]}, {y[x] -> Sqrt[(-1 + 2*E^(2*C[1]) + 2*x^2 + 2*x*Sqrt[-1 + x^2] + E^(4*C[1])*(-1 + 2*x^2 - 2*x*Sqrt[-1 + x^2]))/E^(2*C[1])]/2}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x)^2 = 1-y(x)^2, y(x))
Maple raw output
\verbtime expired||