Step 1: Definition of Carbohydrates: Carbohydrates are biomolecules consisting of carbon, hydrogen, and oxygen, generally following the formula \( C_n(H_2O)_n \). They serve as an energy source and structural material.
Step 2: Differences Between Glucose and Fructose:
Property & Glucose & Fructose
Type & Aldose (Aldehyde group) & Ketose (Ketone group)
Structure & Hexagonal (Pyranose) & Pentagonal (Furanose) Optical Activity & D-Glucose (dextrorotatory) & D-Fructose (levorotatory)
Occurrence & Blood sugar & Found in fruits, honey
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $