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Indian Navy SSR (Sailor) Differential Equations — practice questions

Explore 28 free Differential Equations questions in Indian Navy SSR (Sailor) 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 1–28 of 28.

For dy/dx = x, general solution:Read the answer and worked solution →Solve x dy/dx + y = x²:Read the answer and worked solution →For DE M(x,y) dx + N(x,y) dy = 0 to be EXACT:Read the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →True or false: order and degreeRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Match each method to the form it solvesRead the answer and worked solution →Recognising the typeRead the answer and worked solution →Complete the definition of a differential equationRead the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →Tap every statement true of a general solutionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read 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 →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 →Order the reasoning: from equation to particular solutionRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Reading definitions backRead the answer and worked solution →Which belongs to which idea?Read the answer and worked solution →True or false: what a solution isRead the answer and worked solution →

Worked practice questions

For dy/dx = x, general solution:

  1. y = x²/2 + C
  2. y = 1
  3. y = x
  4. y = e^x
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Correct answer: A. y = x²/2 + C

Integrate: y = x²/2 + C. Constant of integration C means there's a family of solutions need initial condition to fix particular one.

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Solve x dy/dx + y = x²:

  1. y = x²/3 + C/x (linear in y, IF μ = x)
  2. y = x²/3 + C/x
  3. y = x²
  4. y = x + C
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Correct answer: A. y = x²/3 + C/x (linear in y, IF μ = x)

**Divide by x:** dy/dx + y/x = x. P = 1/x, μ = e^(ln x) = x. (xy)' = x · x = x². We have xy = x³/3 + C → y. So xy = x²/3 + C/x.

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For DE M(x,y) dx + N(x,y) dy = 0 to be EXACT:

  1. Always M = N
  2. Linear
  3. ∂M/∂y = ∂N/∂x (exactness condition)
  4. M + N = 0
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Correct answer: C. ∂M/∂y = ∂N/∂x (exactness condition)

**Exact DE:** ∂M/∂y = ∂N/∂x. Then ∃ F(x,y) with dF = M dx + N dy, solution F(x,y) = C. If not exact, find integrating factor.

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