Home › CBSE Class 12 › Calculus › Find the order and degree of the differential eq…
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.
Related questions
A tank is draining and a student is asked how fast the depth falls when the volume is chanThe notation used for a family of antiderivatives, complete with its constant, is the:Knowing an object's velocity, a student recovers its position by finding an:A function whose derivative is the given function is called its:Calculators and computers rely on that same tangent-based idea when they find:An iterative technique for finding zeroes, built on tangent line approximations, is:The rule that resolves such a limit by differentiating numerator and denominator separatelA limit produces the form zero over zero, so its behaviour cannot be read off directly. Th