ODE
\[ 2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.17704 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {2 x^2+\sqrt {2} c_1}{2 \sqrt {1-x}}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {x^{2}}{\sqrt {1-x}}+\frac {\textit {\_C1}}{\sqrt {x -1}}\right ]\] 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))
Maple raw output
[y(x) = x^2/(1-x)^(1/2)+1/(x-1)^(1/2)*_C1]