ODE
\[ y'(x)^2=y(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.174342 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {1}{4} (x-c_1){}^2\right \},\left \{y(x)\to \frac {1}{4} (x+c_1){}^2\right \}\right \}\]
Maple ✓
cpu = 0.162 (sec), leaf count = 23
\[\left [y \left (x \right ) = 0, y \left (x \right ) = \frac {1}{4} x^{2}-\frac {1}{2} x \textit {\_C1} +\frac {1}{4} \textit {\_C1}^{2}\right ]\] 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))
Maple raw output
[y(x) = 0, y(x) = 1/4*x^2-1/2*x*_C1+1/4*_C1^2]