4.29.1 \((1-x) y''(x)+x y'(x)-y(x)=0\)

ODE
\[ (1-x) y''(x)+x y'(x)-y(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0167708 (sec), leaf count = 17

\[\left \{\left \{y(x)\to c_1 e^x-c_2 x\right \}\right \}\]

Maple
cpu = 0.03 (sec), leaf count = 12

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x+{\it \_C2}\,{{\rm e}^{x}} \right \} \] Mathematica raw input

DSolve[-y[x] + x*y'[x] + (1 - x)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^x*C[1] - x*C[2]}}

Maple raw input

dsolve((1-x)*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x+_C2*exp(x)