ODE
\[ x^2 (a+b+c+3) y'''(x)+x^3 y''''(x)+x (a b+a c+a+b c+b+c+1) y''(x)-y'(x) (x-a b c)-k y(x)=0 \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.313593 (sec), leaf count = 146
\[\left \{\left \{y(x)\to x \left ((-1)^{1-a} c_2 x^{-a} \, _1F_3(-a+k+1;2-a,-a+b+1,-a+c+1;x)+(-1)^{1-b} c_3 x^{-b} \, _1F_3(-b+k+1;2-b,a-b+1,-b+c+1;x)+(-1)^{1-c} c_4 x^{-c} \, _1F_3(-c+k+1;2-c,a-c+1,b-c+1;x)\right )+c_1 \, _1F_3(k;a,b,c;x)\right \}\right \}\]
Maple ✓
cpu = 0.111 (sec), leaf count = 123
\[[y \left (x \right ) = \textit {\_C1} \hypergeom \left (\left [k \right ], \left [a , b , c\right ], x\right )+\textit {\_C2} \,x^{1-a} \hypergeom \left (\left [1-a +k \right ], \left [2-a , -a +c +1, b -a +1\right ], x\right )+\textit {\_C3} \,x^{1-b} \hypergeom \left (\left [1-b +k \right ], \left [-b +2, 1+a -b , 1-b +c \right ], x\right )+\textit {\_C4} \,x^{-c +1} \hypergeom \left (\left [1-c +k \right ], \left [-c +2, 1-c +b , a -c +1\right ], x\right )]\] Mathematica raw input
DSolve[-(k*y[x]) - (-(a*b*c) + x)*y'[x] + (1 + a + b + a*b + c + a*c + b*c)*x*y''[x] + (3 + a + b + c)*x^2*y'''[x] + x^3*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*HypergeometricPFQ[{k}, {a, b, c}, x] + x*(((-1)^(1 - a)*C[2]*HypergeometricPFQ[{1 - a + k}, {2 - a, 1 - a + b, 1 - a + c}, x])/x^a + ((-1)^(1 - b)*C[3]*HypergeometricPFQ[{1 - b + k}, {2 - b, 1 + a - b, 1 - b + c}, x])/x^b + ((-1)^(1 - c)*C[4]*HypergeometricPFQ[{1 - c + k}, {2 - c, 1 + a - c, 1 + b - c}, x])/x^c)}}
Maple raw input
dsolve(x^3*diff(diff(diff(diff(y(x),x),x),x),x)+(3+a+b+c)*x^2*diff(diff(diff(y(x),x),x),x)+(a*b+a*c+b*c+a+b+c+1)*x*diff(diff(y(x),x),x)-(-a*b*c+x)*diff(y(x),x)-k*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*hypergeom([k],[a, b, c],x)+_C2*x^(1-a)*hypergeom([1-a+k],[2-a, -a+c+1, b-a+1],x)+_C3*x^(1-b)*hypergeom([1-b+k],[-b+2, 1+a-b, 1-b+c],x)+_C4*x^(-c+1)*hypergeom([1-c+k],[-c+2, 1-c+b, a-c+1],x)]