4.6.46 \(\left (1-x^2\right ) y'(x)=a+4 x y(x)\)

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

\[ \left \{ y \relax (x ) ={\frac {1}{ \left (-1+x \right ) ^{2} \left (1+x \right ) ^{2}} \left (-a \left ({\frac {{x}^{3}}{3}}-x \right ) +{\it \_C1} \right ) } \right \} \] 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