ODE
\[ y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.00772254 (sec), leaf count = 72
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {c_1+x}\right \},\left \{y(x)\to \sqrt {2} \sqrt {c_1+x}\right \},\left \{y(x)\to -\sqrt {2 c_1+x^2}\right \},\left \{y(x)\to \sqrt {2 c_1+x^2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 29
\[ \left \{ -{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0, \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}-2\,x=0 \right \} \] Mathematica raw input
DSolve[x - (1 + x)*y[x]*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2]*Sqrt[x + C[1]])}, {y[x] -> Sqrt[2]*Sqrt[x + C[1]]}, {y[x] -> -Sqrt[x^2 + 2*C[1]]}, {y[x] -> Sqrt[x^2 + 2*C[1]]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2-(1+x)*y(x)*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
y(x)^2-_C1-2*x = 0, -x^2+y(x)^2-_C1 = 0