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$\frac{dy}{dx}$, e^$\frac{dy}{dx}$, ln($d^{2y}$/$dx^2$), or fractional powers of derivative expressions, the degree is NOT DEFINED. Common trap: $d^{2y}$/$dx^2$ = sqrt(1 + $\frac{dy}{dx}$^2). This has order 2 but degree is not defined in this form. After squaring: ($d^{2y}$/$dx^2$)^2 = 1 + $\frac{dy}{dx}$^2, the degree becomes 2. JEE frequently tests this distinction. Another example: sin$\frac{dy}{dx}$ = x has order 1 but undefined degree because sin is not a polynomial operation on dy/dx.