2.1492   ODE No. 1492

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (4 x (n-m)+m (2 m-1)+2 x^2\right ) y'(x)-2 n (-2 m+2 x+1) y(x)-3 x (x-m) y''(x)+x^2 y^{(3)}(x)=0 \] Mathematica : cpu = 0.391762 (sec), leaf count = 43

\[\left \{\left \{y(x)\to c_2 U(-n,m,x) L_n^{m-1}(x)+c_1 U(-n,m,x)^2+c_3 L_n^{m-1}(x){}^2\right \}\right \}\] Maple : cpu = 0.141 (sec), leaf count = 39

\[\{y \left (x \right ) = c_{1} \KummerM \left (-n , m , x\right )^{2}+c_{2} \KummerU \left (-n , m , x\right )^{2}+c_{3} \KummerM \left (-n , m , x\right ) \KummerU \left (-n , m , x\right )\}\]