ODE
\[ y(x)^2 y'(x)^2=a^2 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.00769119 (sec), leaf count = 85
\[\left \{\left \{y(x)\to -\sqrt {2} \sqrt {c_1-a x}\right \},\left \{y(x)\to \sqrt {2} \sqrt {c_1-a x}\right \},\left \{y(x)\to -\sqrt {2} \sqrt {a x+c_1}\right \},\left \{y(x)\to \sqrt {2} \sqrt {a x+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 29
\[ \left \{ -2\,ax+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0,2\,ax+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y[x]^2*y'[x]^2 == a^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2]*Sqrt[-(a*x) + C[1]])}, {y[x] -> Sqrt[2]*Sqrt[-(a*x) + C[1]]}, {y[x] -> -(Sqrt[2]*Sqrt[a*x + C[1]])}, {y[x] -> Sqrt[2]*Sqrt[a*x + C[1]]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2 = a^2, y(x),'implicit')
Maple raw output
-2*a*x+y(x)^2-_C1 = 0, 2*a*x+y(x)^2-_C1 = 0