ODE
\[ x \left (1-x^2\right ) y'(x)=a x^2+y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0169882 (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 = 0.024 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) =-{\frac {ax}{ \left ( -1+x \right ) \left ( 1+x \right ) }\sqrt { \left ( -1+x \right ) \left ( 1+x \right ) }\ln \left ( x+\sqrt {{x}^{2}-1} \right ) }+{{\it \_C1}\,x{\frac {1}{\sqrt {-1+x}}}{\frac {1}{\sqrt {1+x}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/(-1+x)/(1+x)*x*a*((-1+x)*(1+x))^(1/2)*ln(x+(x^2-1)^(1/2))+1/(-1+x)^(1/2)/(1+x)^(1/2)*x*_C1