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JEE Advanced Differential Equations — practice questions — page 3

Explore 70 free Differential Equations questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Differential Equations questions and exercises with answers

Showing questions 61–70 of 70.

Match each term to its meaningRead the answer and worked solution →Flip and pair: form with nameRead the answer and worked solution →True or false: what a solution isRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Recognising the typeRead the answer and worked solution →True or false: methods of solutionRead the answer and worked solution →Order, degree, or neither?Read the answer and worked solution →Complete the definition of a differential equationRead the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Read the answer and worked solution →

Worked practice questions

Match each term to its meaning

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Matching pairs
  1. Left
    Dependent variable
    Right
    the one being differentiated
  2. Left
    Independent variable
    Right
    the one differentiated with respect to
  3. Left
    Order
    Right
    order of the highest derivative
The vocabulary the rest of the chapter assumes. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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Flip and pair: form with name

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Matching pairs
  1. A
    dy/dx + Py = Q
    B
    first order linear
  2. A
    Terms split as f(y)dy = g(x)dx
    B
    variable separable
  3. A
    f(x, y) homogeneous of degree zero
    B
    homogeneous equation
  4. A
    Solution with no constants
    B
    particular solution
  5. A
    Solution with n constants
    B
    general solution
Recognising a form by sight. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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True or false: what a solution is

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Questions
  1. Statement is true
    Yes
    Statement
    A solution is a function that satisfies the equation.
  2. Statement is true
    Yes
    Statement
    A general solution describes a family of solutions.
  3. Statement is true
    Yes
    Statement
    A particular solution is obtained from a given condition.
  4. Statement is true
    No
    Statement
    A solution must be a polynomial.
  5. Statement is true
    No
    Statement
    An equation can have only one solution.
The definition is simpler than people expect, and that is the point. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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