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 = 0.045262 (sec), leaf count = 78
\[\left \{\left \{y(x)\to 2^{5/8} c_1 e^{x-\frac {1}{2}}-\frac {2^{3/8} c_2 e^{\frac {x}{2}-\frac {1}{4}}}{\sqrt [4]{2 x-1}}+\frac {c_2 e^{x-\frac {1}{2}} \Gamma \left (\frac {3}{4},\frac {1}{4} (2 x-1)\right )}{\sqrt [8]{2}}\right \}\right \}\]
Maple ✓
cpu = 0.119 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={1{{\rm e}^{{\frac {x}{2}}}} \left ( {{\sl U}\left (1,\,{\frac {3}{4}},\,-{\frac {1}{4}}+{\frac {x}{2}}\right )}{\it \_C2}+{{\sl M}\left (1,\,{\frac {3}{4}},\,-{\frac {1}{4}}+{\frac {x}{2}}\right )}{\it \_C1} \right ) {\frac {1}{\sqrt [4]{-1+2\,x}}}} \right \} \] 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] -> 2^(5/8)*E^(-1/2 + x)*C[1] - (2^(3/8)*E^(-1/4 + x/2)*C[2])/(-1 + 2*x)^(1/4) + (E^(-1/2 + x)*C[2]*Gamma[3/4, (-1 + 2*x)/4])/2^(1/8)}}
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),'implicit')
Maple raw output
y(x) = exp(1/2*x)*(KummerU(1,3/4,-1/4+1/2*x)*_C2+KummerM(1,3/4,-1/4+1/2*x)*_C1)/(-1+2*x)^(1/4)