DSolve[-(h[x]*(-f[x] + y[x])*(-g[x] + y[x])*(-((a*f[x] + b*g[x])/(a + b)) + y[x])) - ((-g[x] + y[x])*Derivative[1][f][x])/(f[x] - g[x]) - ((-f[x] + y[x])*Derivative[1][g][x])/(-f[x] + g[x]) + Derivative[1][y][x] == 0,y[x],x]