Get Answers to all your Questions

header-bg qa

Explain solution RD Sharma class 12 chapter Differential Equations exercise 21.7 question 45 sub question (iv)  maths

Answers (1)


Answer: \sin y=e^{x}

Hint: Separate the terms of x and y and then integrate them.

Given: \cos y \frac{d y}{d x}=e^{x}, y(0)=\frac{\pi}{2}


        \begin{aligned} &\cos y \frac{d y}{d x}=e^{x} \\\\ &\cos y d y=e^{x} d x \end{aligned}

        Integrating both sides

        \begin{aligned} &\int \cos y d y=\int e^{x} d x \\\\ &\sin y=e^{x}+c \end{aligned}                ..............(1)

        Given that  y(0)=\frac{\pi}{2} \text { i.e. at } x=0, y=\frac{\pi}{2}

        \begin{aligned} &\therefore \sin \frac{\pi}{2}=e^{0}+c \quad[\therefore o f(1)] \\\\ &\qquad \Rightarrow 1=1+c \Rightarrow c=0\left[\therefore \sin \frac{\pi}{2}=1, e^{0}=1\right] \end{aligned}

        Put in (1) we get

        \sin y=e^{x}+0 \Rightarrow \sin y=e^{x}

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support