4.16.15 $y^{\prime }(x{)}^2=(y(x)-1)y(x{)}^2$

ODE
$$y^{\prime }(x{)}^2=(y(x)-1)y(x{)}^2$$ ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for $y^{\prime }$

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

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

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

$$\{x-2\arctan \left(\sqrt{y\left(x\right)-1}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,x+2\arctan \left(\sqrt{y\left(x\right)-1}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=1\}$$ 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