60.3.282 problem 1287

Internal problem ID [11292]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1287
Date solved : Monday, January 27, 2025 at 11:05:21 PM
CAS classification : [_Jacobi]

\begin{align*} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(9*x*(x-1)*diff(diff(y(x),x),x)+3*(2*x-1)*diff(y(x),x)-20*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \left (6 x -5\right ) x^{{2}/{3}}+c_{2} \left (6 x -1\right ) \left (x -1\right )^{{2}/{3}} \]

✓ Solution by Mathematica

Time used: 0.530 (sec). Leaf size: 93

DSolve[-20*y[x] + 3*(-1 + 2*x)*D[y[x],x] + 9*(-1 + x)*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (3 c_2 (x-1) \operatorname {Gamma}\left (\frac {4}{3}\right ) Q_1^{\frac {2}{3}}(2 x-1)+c_1 (5-6 x) (1-x)^{2/3} \sqrt [3]{x}\right ) \exp \left (\int _1^x\frac {1-2 K[1]}{3 K[1]-3 K[1]^2}dK[1]\right )}{3 (x-1) \operatorname {Gamma}\left (\frac {4}{3}\right )} \]