ODE
\[ y'(x)=x^n \left (a+b y(x)^2\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.328543 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} \left (\frac {x^{n+1}}{n+1}+c_1\right )\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.058 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\tan \left (\frac {\sqrt {a b}\, \left (\textit {\_C1} n +x^{n +1}+\textit {\_C1} \right )}{n +1}\right ) \sqrt {a b}}{b}\right ]\] Mathematica raw input
DSolve[y'[x] == x^n*(a + b*y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[a]*Tan[Sqrt[a]*Sqrt[b]*(x^(1 + n)/(1 + n) + C[1])])/Sqrt[b]}}
Maple raw input
dsolve(diff(y(x),x) = x^n*(a+b*y(x)^2), y(x))
Maple raw output
[y(x) = tan((a*b)^(1/2)*(_C1*n+x^(n+1)+_C1)/(n+1))*(a*b)^(1/2)/b]