2.33   ODE No. 33

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

y(x)2f(x)g(x)+g(x)f(x)+y(x)=0 Mathematica : cpu = 0.48339 (sec), leaf count = 160

Solve[1y(x)(1(g(x)+f(x)K[2])21x(2(f(K[1])K[2]2f(K[1])g(K[1])g(K[1]))g(K[1])(g(K[1])+f(K[1])K[2])32K[2]f(K[1])g(K[1])(g(K[1])+f(K[1])K[2])2)dK[1])dK[2]+1xf(K[1])y(x)2f(K[1])g(K[1])g(K[1])f(K[1])g(K[1])(g(K[1])+f(K[1])y(x))2dK[1]=c1,y(x)] Maple : cpu = 0.457 (sec), leaf count = 58

{y(x)=c1f(x)g(x)f(x)g(x)(ddxf(x)f(x)2g(x)dx)1(c1+ddxf(x)f(x)2g(x)dx)f(x)2}

Hand solution

fgy2+gf+y=0y=gf+fgy2(1)=P(x)+Q(x)y+R(x)y2

This is Ricatti first order non-linear ODE. P(x)=gf,Q(x)=0,R(x)=fg.

To do.