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HPCET Variables Separable — practice questions

Explore 29 free Variables Separable questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Variables Separable questions and exercises with answers

Showing questions 1–29 of 29.

Solve $\dfrac{dy}{dx} = \dfrac{1 + y^2}{1 + x^2}$.Read the answer and worked solution →Solve $\dfrac{dy}{dx} = e^{x+y}$.Read the answer and worked solution →The DE $y - x \dfrac{dy}{dx} = 0$ has general solution:Read the answer and worked solution →Solve $\sec^2 x \cdot \tan y \, dx + \sec^2 y \cdot \tan x \, dy = 0$: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

Solve $\dfrac{dy}{dx} = \dfrac{1 + y^2}{1 + x^2}$.

  1. $\tan^{-1}y = \tan^{-1}x + c$
  2. $\tan^{-1}y - \tan^{-1}x = 0$
  3. $y = x + c$
  4. $y^2 = x^2 + c$
Show answer and solution

Correct answer: A. $\tan^{-1}y = \tan^{-1}x + c$

**Variables separable:** $dy/(1+y^2) = dx/(1+x^2)$. **Integrating:** $\tan^{-1}y = \tan^{-1}x + c$.

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Solve $\dfrac{dy}{dx} = e^{x+y}$.

  1. $e^{-y} = -e^x + c$
  2. $e^y = e^x + c$
  3. $y = e^x + c$
  4. $\log y = x + c$
Show answer and solution

Correct answer: A. $e^{-y} = -e^x + c$

$dy/e^y = e^x\,dx$ ⇒ $\int e^{-y}\,dy = \int e^x\,dx$ ⇒ $-e^{-y} = e^x + c'$ ⇒ $e^{-y} = -e^x + c$.

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The DE $y - x \dfrac{dy}{dx} = 0$ has general solution:

  1. $y = cx$
  2. $y = c/x$
  3. $y = c e^x$
  4. $y^2 = c x$
Show answer and solution

Correct answer: A. $y = cx$

**Rewrite:** $dy/y = dx/x$. **Integrating:** $\log y = \log x + \log c$ ⇒ $y = cx$ (family of straight lines through origin).

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More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations