The order of a differential equation is the order of the highest derivative present. The degree is the exponent of the highest order derivative, BUT only when the equation is expressed as a polynomial in the derivatives. If the equation involves sin(dy/dx), e^(dy/dx), ln(d^2y/dx^2), or fractional powers of derivative expressions, the degree is NOT DEFINED. Common trap: d^2y/dx^2 = sqrt(1 + (dy/dx)^2). This has order 2 but degree is not defined in this form. After squaring: (d^2y/dx^2)^2 = 1 + (dy/dx)^2, the degree becomes 2. JEE frequently tests this distinction. Another example: sin(dy/dx) = x has order 1 but undefined degree because sin is not a polynomial operation on dy/dx.