ODE
\[ \left (1-x^2\right ) y'(x)=a+4 x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00616223 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {3 c_1-a x \left (x^2-3\right )}{3 \left (x^2-1\right )^2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\frac {1}{ \left ( -1+x \right ) ^{2} \left ( 1+x \right ) ^{2}} \left ( -a \left ( {\frac {{x}^{3}}{3}}-x \right ) +{\it \_C1} \right ) } \right \} \] 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),'implicit')
Maple raw output
y(x) = (-a*(1/3*x^3-x)+_C1)/(-1+x)^2/(1+x)^2