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ISC Class 12 Differential Equations — practice questions — page 2

Explore 50 free Differential Equations questions in ISC Class 12 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 31–50 of 50.

The DE dy/dx = y/x is best solved by:Read the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:Read the answer and worked solution →Order the reasoning: from equation to particular solutionRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Counting arbitrary constantsRead the answer and worked solution →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 →A rational function p(x)/q(x) is continuous at every x where what holds?Read the answer and worked solution →A continuous function on a closed interval [a, b] always attains what?Read the answer and worked solution →On which interval is f(x) = cos x strictly decreasing?Read the answer and worked solution →x + 1/x slopes downward on which interval?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

The DE dy/dx = y/x is best solved by:

  1. Variable separable (the easiest first try)
  2. Bernoulli's substitution v = y^(1−n)
  3. Integrating factor as linear DE
  4. Auxiliary equation as second-order
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Correct answer: A. Variable separable (the easiest first try)

We have dy/dx = y/x → dy/y. That is dy/dx = dx/x → ln|y|. That is dy/dx = ln|x| + C → y. So dy/dx = Ax. **Variable separable:** separate variables, integrate both sides.

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Order the steps: solve by separating variables

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Steps
  1. Check that x and y terms can be separated completely
  2. Move every y term to the side carrying dy
  3. Move every x term to the side carrying dx
  4. Integrate both sides
  5. Add the arbitrary constant to obtain the general solution
The method Leibnitz discovered, as the chapter sets it out. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:

  1. Order 3, degree 2
  2. Order 2, degree 3
  3. Order 5, degree 1
  4. Order 2, degree 5
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Correct answer: B. Order 2, degree 3

Order = highest derivative present = d²y/dx² → 2. Degree = power of highest-order derivative = (d²y/dx²)³ → 3.

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