Internal problem ID [9595]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1260.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }=-\operatorname {a1} \operatorname {b1} \operatorname {d1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 76
dsolve(x*(x-1)*diff(diff(y(x),x),x)+((a1+b1+1)*x-d1)*diff(y(x),x)+a1*b1*d1=0,y(x), singsol=all)
\[ y \left (x \right ) = \int \left (-\operatorname {a1} \operatorname {b1} \operatorname {signum}\left (x -1\right )^{\operatorname {a1} +\operatorname {b1} -\operatorname {d1}} \left (-\operatorname {signum}\left (x -1\right )\right )^{-\operatorname {a1} -\operatorname {b1} +\operatorname {d1}} \operatorname {hypergeom}\left (\left [\operatorname {d1} , -\operatorname {a1} -\operatorname {b1} +\operatorname {d1} \right ], \left [1+\operatorname {d1} \right ], x\right )+x^{-\operatorname {d1}} c_{1} \right ) \left (x -1\right )^{-\operatorname {a1} -\operatorname {b1} -1+\operatorname {d1}}d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.618 (sec). Leaf size: 65
DSolve[a1*b1*d1 + (-d1 + (1 + a1 + b1)*x)*y'[x] + (-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {a1} \text {b1} x \operatorname {Gamma}(\text {d1}+1) \, _3\tilde {F}_2(1,\text {a1}+\text {b1}+1,1;\text {d1}+1,2;x)-\frac {c_1 x^{1-\text {d1}} \operatorname {Hypergeometric2F1}(1-\text {d1},\text {a1}+\text {b1}-\text {d1}+1,2-\text {d1},x)}{\text {d1}-1}+c_2 \]