ODE
\[ x \left (1-x^2\right ) y'(x)=a x^2+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.168243 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {x \left (a \sin ^{-1}(x)+c_1\right )}{\sqrt {1-x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 51
\[\left [y \left (x \right ) = -\frac {x a \sqrt {\left (x -1\right ) \left (1+x \right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (1+x \right )}+\frac {x \textit {\_C1}}{\sqrt {x -1}\, \sqrt {1+x}}\right ]\] Mathematica raw input
DSolve[x*(1 - x^2)*y'[x] == a*x^2 + y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x*(a*ArcSin[x] + C[1]))/Sqrt[1 - x^2]}}
Maple raw input
dsolve(x*(-x^2+1)*diff(y(x),x) = a*x^2+y(x), y(x))
Maple raw output
[y(x) = -1/(x-1)/(1+x)*x*a*((x-1)*(1+x))^(1/2)*ln(x+(x^2-1)^(1/2))+1/(x-1)^(1/2)/(1+x)^(1/2)*x*_C1]