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

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

[_quadrature]

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

Mathematica
cpu = 0.0217739 (sec), leaf count = 35

\[\left \{\left \{y(x)\to \sec ^2\left (\frac {1}{2} \left (x-c_1\right )\right )\right \},\left \{y(x)\to \tan ^2\left (\frac {1}{2} \left (c_1+x\right )\right )+1\right \}\right \}\]

Maple
cpu = 0.035 (sec), leaf count = 37

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

DSolve[y'[x]^2 == (-1 + y[x])*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> Sec[(x - C[1])/2]^2}, {y[x] -> 1 + Tan[(x + C[1])/2]^2}}

Maple raw input

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

Maple raw output

y(x) = 1, x-2*arctan((y(x)-1)^(1/2))-_C1 = 0, x+2*arctan((y(x)-1)^(1/2))-_C1 = 0