4.16.30 \(y'(x)^2-7 y'(x)+12=0\)

ODE
\[ y'(x)^2-7 y'(x)+12=0 \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Both independent and dependent variable missing

Mathematica
cpu = 0.00231956 (sec), leaf count = 21

\[\left \{\left \{y(x)\to c_1+3 x\right \},\left \{y(x)\to c_1+4 x\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 17

\[ \left \{ y \relax (x ) =3\,x+{\it \_C1},y \relax (x ) =4\,x+{\it \_C1} \right \} \] Mathematica raw input

DSolve[12 - 7*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> 3*x + C[1]}, {y[x] -> 4*x + C[1]}}

Maple raw input

dsolve(diff(y(x),x)^2-7*diff(y(x),x)+12 = 0, y(x),'implicit')

Maple raw output

y(x) = 4*x+_C1, y(x) = 3*x+_C1