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NDA 2020 Maths · Mathematics · Differential Equations · easy

The differential equation dy/dx+xy^2=x^2 is linear. 2. The differential equation dy/dx=e^xsin y can be solved by separating the variables.

Single correct option

Consider the following statements:
1. The differential equation dydx+xy2=x2\dfrac{dy}{dx}+xy^2=x^2 is linear.
2. The differential equation dydx=exsin⁡y\dfrac{dy}{dx}=e^x\sin y can be solved by separating the variables.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

A linear equation must be of first degree in yy and dydx\dfrac{dy}{dx} with no product like y2y^2; the term xy2xy^2 makes the first equation non-linear, so statement 1 is false. In the second equation, dysin⁡y=ex dx\dfrac{dy}{\sin y}=e^x\,dx separates the variables, so statement 2 is correct. Hence only statement 2 is correct. Linearity concerns the dependent variable, not the independent variable xx.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake