ODE
\[ \left (1-x^2\right ) y'(x)=a+4 x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.17528 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {-a x \left (x^2-3\right )+3 c_1}{3 \left (x^2-1\right )^2}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 29
\[\left [y \left (x \right ) = \frac {-a \left (\frac {1}{3} x^{3}-x \right )+\textit {\_C1}}{\left (x -1\right )^{2} \left (1+x \right )^{2}}\right ]\] Mathematica raw input
DSolve[(1 - x^2)*y'[x] == a + 4*x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-(a*x*(-3 + x^2)) + 3*C[1])/(3*(-1 + x^2)^2)}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x) = a+4*x*y(x), y(x))
Maple raw output
[y(x) = (-a*(1/3*x^3-x)+_C1)/(x-1)^2/(1+x)^2]