ODE
\[ (1-2 x) y''(x)-(4-3 x) y'(x)+(3-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.20725 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\frac {e^{x-\frac {1}{2}} \left (\sqrt [4]{2} c_2 \Gamma \left (-\frac {1}{4},\frac {1}{4} (2 x-1)\right )-8 c_1\right )}{4\ 2^{3/8}}\right \}\right \}\]
Maple ✓
cpu = 0.357 (sec), leaf count = 47
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,{\mathrm e}^{\frac {x}{2}} \KummerM \left (1, \frac {3}{4}, -\frac {1}{4}+\frac {x}{2}\right )}{\left (-1+2 x \right )^{\frac {1}{4}}}+\frac {\textit {\_C2} \,{\mathrm e}^{\frac {x}{2}} \KummerU \left (1, \frac {3}{4}, -\frac {1}{4}+\frac {x}{2}\right )}{\left (-1+2 x \right )^{\frac {1}{4}}}\right ]\] Mathematica raw input
DSolve[(3 - x)*y[x] - (4 - 3*x)*y'[x] + (1 - 2*x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/4*(E^(-1/2 + x)*(-8*C[1] + 2^(1/4)*C[2]*Gamma[-1/4, (-1 + 2*x)/4]))/2^(3/8)}}
Maple raw input
dsolve((1-2*x)*diff(diff(y(x),x),x)-(4-3*x)*diff(y(x),x)+(3-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/2*x)/(-1+2*x)^(1/4)*KummerM(1,3/4,-1/4+1/2*x)+_C2*exp(1/2*x)/(-1+2*x)^(1/4)*KummerU(1,3/4,-1/4+1/2*x)]