60.3.260 problem 1265

Internal problem ID [11270]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1265
Date solved : Tuesday, January 28, 2025 at 05:53:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.387 (sec). Leaf size: 94

dsolve((x-1)*(x-2)*diff(diff(y(x),x),x)-(2*x-3)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (x -2\right )^{2} \left (c_{1} \operatorname {hypergeom}\left (\left [\frac {5}{2}-\frac {\sqrt {5}}{2}, \frac {1}{2}-\frac {\sqrt {5}}{2}\right ], \left [-\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -1\right )^{\frac {\sqrt {5}}{2}}+c_{2} \operatorname {hypergeom}\left (\left [\frac {5}{2}+\frac {\sqrt {5}}{2}, \frac {1}{2}+\frac {\sqrt {5}}{2}\right ], \left [\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -1\right )^{-\frac {\sqrt {5}}{2}}\right )}{\sqrt {x -1}} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 57

DSolve[y[x] - (-3 + 2*x)*D[y[x],x] + (-2 + x)*(-1 + x)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-3 x+2\right ) \left (c_1 P_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)+c_2 Q_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)\right ) \]