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 = 0.198385 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \sec ^2\left (\frac {x-c_1}{2}\right )\right \},\left \{y(x)\to 1+\tan ^2\left (\frac {x+c_1}{2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.135 (sec), leaf count = 20
\[\left [y \left (x \right ) = 1, y \left (x \right ) = \tan ^{2}\left (-\frac {x}{2}+\frac {\textit {\_C1}}{2}\right )+1\right ]\] 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))
Maple raw output
[y(x) = 1, y(x) = tan(-1/2*x+1/2*_C1)^2+1]