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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Differential Equations

NDA 2015 · Mathematics · Differential Equations

What is the solution of the differential equation ((d y)/(d x))-a=0...

What is the solution of the differential equation sin⁡(dydx)−a=0?\sin \left(\frac{d y}{d x}\right)-a=0 ? where cc is an arbitrary constant.

Options

  1. Ay=xsin⁡−1a+cy=x \sin ^{-1} a+c
  2. Bx=ysin⁡−1a+cx=y \sin ^{-1} a+c
  3. Cy=x+xsin⁡−1a+cy=x+x \sin ^{-1} a+c
  4. Dy=sin⁡−1a+cy=\sin ^{-1} a+c

Correct answer

A. y=xsin⁡−1a+cy=x \sin ^{-1} a+c

Step-by-step solution

sin⁡(dydx)−a=0sin⁡(dydx)=a⇒dydx=sin⁡−1ady=sin⁡−1adx Now integrating both sides, ∫dy=∫sin⁡−1adxy=xsin⁡−1a+c∴ Option (A) is correct. \begin{aligned} & \sin \left(\frac{d y}{d x}\right)-a=0 \\ & \sin \left(\frac{d y}{d x}\right)=a \\ & \Rightarrow \quad \frac{\mathrm{dy}}{\mathrm{dx}}=\sin ^{-1} \mathrm{a} \\ & d y=\sin ^{-1} a d x \\ & \text{ Now integrating both sides, } \\ & \int d y=\int \sin ^{-1} a d x \\ & y=x \sin ^{-1} a+c \\ & \therefore \quad \text{ Option (A) is correct. } \end{aligned}
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