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Find the order and degree of the differential equation $\dfrac{d^2y}{dx^2} + 3\left(\dfrac{dy}{dx}\right)^4 + y = \sin x$.
AOrder 1, degree 4
BOrder 4, degree 2
COrder 2, degree 4
DOrder 2, degree 1
Answer & Solution
Correct answer: D. Order 2, degree 1
Order is the order of the highest derivative present, which is $\dfrac{d^2y}{dx^2}$, so order = 2. Degree is the power of that highest-order derivative once the equation is a polynomial in derivatives and free of radicals. The $\dfrac{d^2y}{dx^2}$ term appears to the first power, so degree = 1. The exponent 4 on $dy/dx$ does not affect the degree because it is not the highest-order derivative.
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