4.16.3 \(y'(x)^2=y(x)\)

ODE
\[ y'(x)^2=y(x) \] ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)

Mathematica
cpu = 0.0150853 (sec), leaf count = 31

\[\left \{\left \{y(x)\to \frac {1}{4} \left (x-c_1\right ){}^2\right \},\left \{y(x)\to \frac {1}{4} \left (c_1+x\right ){}^2\right \}\right \}\]

Maple
cpu = 0.034 (sec), leaf count = 31

\[ \left \{ x-2\,\sqrt {y \relax (x ) }-{\it \_C1}=0,x+2\,\sqrt {y \relax (x ) }-{\it \_C1}=0,y \relax (x ) =0 \right \} \] Mathematica raw input

DSolve[y'[x]^2 == y[x],y[x],x]

Mathematica raw output

{{y[x] -> (x - C[1])^2/4}, {y[x] -> (x + C[1])^2/4}}

Maple raw input

dsolve(diff(y(x),x)^2 = y(x), y(x),'implicit')

Maple raw output

y(x) = 0, x-2*y(x)^(1/2)-_C1 = 0, x+2*y(x)^(1/2)-_C1 = 0