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JEE Advanced Unit 7: Differential Equations and Modeling — practice questions — page 2

Explore 38 free Unit 7: Differential Equations and Modeling questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 7: Differential Equations and Modeling questions and exercises with answers

Showing questions 31–38 of 38.

A first-order equation of the form $\dfrac{dy}{dx} = f(x)\,g(y)$ is solved by the method of:Read the answer and worked solution →The general solution of $\dfrac{dy}{dx} = 0$ is:Read the answer and worked solution →The number of arbitrary constants in the general solution of an $n$-th order differential equation is:Read the answer and worked solution →The general solution of $\dfrac{dy}{dx} = 2x$ is:Read the answer and worked solution →The standard form of a first-order linear differential equation is:Read the answer and worked solution →The degree of the differential equation $\left(\dfrac{dy}{dx}\right)^2 + y = 0$ is:Read the answer and worked solution →The general solution of $\dfrac{dy}{dx} = e^x$ is:Read the answer and worked solution →The order of the differential equation $\dfrac{d^2y}{dx^2} + 3\dfrac{dy}{dx} + 2y = 0$ is:Read the answer and worked solution →

Worked practice questions

A first-order equation of the form $\dfrac{dy}{dx} = f(x)\,g(y)$ is solved by the method of:

  1. substitution of constants
  2. partial fractions
  3. integration by parts
  4. variable separation
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Correct answer: D. variable separation

Equations of the form dy/dx = f(x)g(y) are solved by separating variables.

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The general solution of $\dfrac{dy}{dx} = 0$ is:

  1. $y = x + C$
  2. $y = 0$
  3. $y = x$
  4. $y = C$
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Correct answer: D. $y = C$

dy/dx = 0 integrates to y = C, a constant.

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The number of arbitrary constants in the general solution of an $n$-th order differential equation is:

  1. $1$
  2. $2n$
  3. $n-1$
  4. $n$
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Correct answer: D. $n$

An n-th order differential equation's general solution carries n arbitrary constants.

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