4.6.46 $(1-x^2)y^{\prime }(x)=a+4xy(x)$

ODE
$$(1-x^2)y^{\prime }(x)=a+4xy(x)$$ ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica ✓
cpu = 0.00616223 (sec), leaf count = 30

$$\left\{\{y(x)\to \frac{3c_1-ax(x^2-3)}{3{(x^2-1)}^2}\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 29

$$\{y\left(x\right)=\frac{1}{{(-1+x)}^2{(1+x)}^2}(-a(\frac{x^3}{3}-x)+\mathit{\_}\mathit{C}\mathit{1})\}$$ 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