60.3.289 problem 1294

Internal problem ID [11299]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1294
Date solved : Tuesday, January 28, 2025 at 05:58:01 PM
CAS classification : [_Jacobi]

\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.234 (sec). Leaf size: 33

dsolve(144*x*(x-1)*diff(diff(y(x),x),x)+(168*x-96)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \left (\operatorname {LegendreP}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_{1} +\operatorname {LegendreQ}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_{2} \right ) x^{{1}/{6}} \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 44

DSolve[y[x] + (-96 + 168*x)*D[y[x],x] + 144*(-1 + x)*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{12},\frac {1}{12},\frac {2}{3},x\right )+\sqrt [3]{-1} c_2 \sqrt [3]{x} \operatorname {Hypergeometric2F1}\left (\frac {5}{12},\frac {5}{12},\frac {4}{3},x\right ) \]