ODE
\[ y'(x)^2=a x^n \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.153299 (sec), leaf count = 57
\[\left \{\left \{y(x)\to -\frac {2 \sqrt {a} x^{\frac {n}{2}+1}}{n+2}+c_1\right \},\left \{y(x)\to \frac {2 \sqrt {a} x^{\frac {n}{2}+1}}{n+2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.096 (sec), leaf count = 41
\[\left [y \left (x \right ) = \frac {2 x \sqrt {a \,x^{n}}}{2+n}+\textit {\_C1}, y \left (x \right ) = -\frac {2 x \sqrt {a \,x^{n}}}{2+n}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[y'[x]^2 == a*x^n,y[x],x]
Mathematica raw output
{{y[x] -> (-2*Sqrt[a]*x^(1 + n/2))/(2 + n) + C[1]}, {y[x] -> (2*Sqrt[a]*x^(1 + n/2))/(2 + n) + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2 = a*x^n, y(x))
Maple raw output
[y(x) = 2*x/(2+n)*(a*x^n)^(1/2)+_C1, y(x) = -2*x/(2+n)*(a*x^n)^(1/2)+_C1]