How do I find the order and degree of a differential equation, and why do they matter?
The order is simply the highest derivative that appears (a d²y/dx² makes it second order).
The order is simply the highest derivative that appears (a d²y/dx² makes it second order). The degree is the power of that highest derivative — but only after you clear any radicals or fractional powers involving derivatives. For example, if a square root of dy/dx appears, square the equation first, then read off the degree. Order and degree classify the equation and tell you how many arbitrary constants its general solution will carry (equal to the order).
Key point
Order = highest derivative present; degree = its power after removing radicals/fractions in derivatives.
Common mistake
reading the degree while a derivative is still under a root.
Memory tip
rationalise the derivatives first, then order = highest, degree = its power.
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