60.3.252 problem 1257

Internal problem ID [11262]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1257
Date solved : Monday, January 27, 2025 at 11:00:52 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(x*(x-1)*diff(diff(y(x),x),x)+((a+1)*x+b)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +x^{b +1} \operatorname {hypergeom}\left (\left [b +1, b +a +1\right ], \left [b +2\right ], x\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 48

DSolve[(b + (1 + a)*x)*D[y[x],x] + (-1 + x)*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\exp \left (\int _1^{K[2]}\frac {b+a K[1]+K[1]}{K[1]-K[1]^2}dK[1]\right ) c_1dK[2]+c_2 \]