4.5.47 \(2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x\)

ODE
\[ 2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0116151 (sec), leaf count = 32

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

Maple
cpu = 0.01 (sec), leaf count = 23

\[ \left \{ y \relax (x ) ={{x}^{2}{\frac {1}{\sqrt {1-x}}}}+{{\it \_C1}{\frac {1}{\sqrt {-1+x}}}} \right \} \] Mathematica raw input

DSolve[2*(1 - x)*y'[x] == 4*Sqrt[1 - x]*x + y[x],y[x],x]

Mathematica raw output

{{y[x] -> (2*x^2 + Sqrt[2]*C[1])/(2*Sqrt[1 - x])}}

Maple raw input

dsolve(2*(1-x)*diff(y(x),x) = 4*x*(1-x)^(1/2)+y(x), y(x),'implicit')

Maple raw output

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