ODE
\[ x^2 y'(x)=a+b y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.239941 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\frac {\sqrt {a} \tan \left (\frac {\sqrt {a} \sqrt {b} (1-c_1 x)}{x}\right )}{\sqrt {b}}\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 28
\[\left [y \left (x \right ) = \frac {\tan \left (\frac {\sqrt {a b}\, \left (x \textit {\_C1} -1\right )}{x}\right ) \sqrt {a b}}{b}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == a + b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -((Sqrt[a]*Tan[(Sqrt[a]*Sqrt[b]*(1 - x*C[1]))/x])/Sqrt[b])}}
Maple raw input
dsolve(x^2*diff(y(x),x) = a+b*y(x)^2, y(x))
Maple raw output
[y(x) = tan((a*b)^(1/2)*(_C1*x-1)/x)*(a*b)^(1/2)/b]