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Mathematics · JEE | DIFFERENTIAL EQUATIONS

हिन्दी

Consider the following statements regarding differential equations: (A) The degree of a differential equation is always defined if it is a polynomial equation in its derivatives. (B) The order of a differential equation is the order of the highest order derivative occurring in the equation. (C) A solution free from arbitrary constants is called a particular solution. (D) The number of arbitrary constants in the general solution of a first-order differential equation is always two. Which of the above statements are correct?

  1. A
    (A), (B) and (C) only
  2. B
    and (D) only
  3. C
    (B), (C) and (D) only
  4. D
    All of the above
View Answer & Solution

Correct answer · Option A

(A), (B) and (C) only

Explanation

Statements (A), (B), and (C) are correct textbook definitions. Statement (D) is incorrect because a first-order differential equation has only one arbitrary constant in its general solution.

Related questions

Given below are two statements: Statement I: A homogeneous differential equation can always be reduced to a separable variable form by substituting \( y = vx \). Statement II: The integrating factor of the differential equation \( \frac{dy}{dx} + y \sec x = \tan x \) is \( \sec x + \tan x \). In the light of the above statements, choose the most appropriate answer from the options given below:→Consider the following statements regarding differential equations: (A) A homogeneous differential equation of degree zero can always be solved by substituting \( y = vx \). (B) The integrating factor (I.F.) for the linear differential equation \( \frac{dy}{dx} + Py = Q \) is given by \( e^{\int P \, dx} \). (C) The general solution of \( \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \) contains a logarithmic term. (D) If \( M \, dx + N \, dy = 0 \) is homogeneous, the substitution \( x = vy \) is also valid. Which of the above statements are correct?→What is the equation of the curve passing through the point \( (-2, 3) \) given that the slope of the tangent to the curve at any point \( (x, y) \) is \( \frac{2x}{y^2} \)?→If \( y = c (x^2 + y^2)^2 \) is the general solution of a differential equation, the order of that differential equation is:→
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