4.6.32 \(\left (1-x^2\right ) y'(x)=5-x y(x)\)

ODE
\[ \left (1-x^2\right ) y'(x)=5-x y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0125513 (sec), leaf count = 21

\[\left \{\left \{y(x)\to c_1 \sqrt {x^2-1}+5 x\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 20

\[ \left \{ y \relax (x ) =\sqrt {-1+x}\sqrt {1+x}{\it \_C1}+5\,x \right \} \] Mathematica raw input

DSolve[(1 - x^2)*y'[x] == 5 - x*y[x],y[x],x]

Mathematica raw output

{{y[x] -> 5*x + Sqrt[-1 + x^2]*C[1]}}

Maple raw input

dsolve((-x^2+1)*diff(y(x),x) = 5-x*y(x), y(x),'implicit')

Maple raw output

y(x) = (-1+x)^(1/2)*(1+x)^(1/2)*_C1+5*x