Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 34

Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 34

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of exponential and cos inverse function

Given:

y=e^{a \cos ^{-1} x} , \text { prove }\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-a^{2} y=0

Solution:

y=e^{a \cos ^{-1} x}

        \begin{aligned} &\text { Taking logarithm both sides }\\ &\log y=a \cos ^{-1} x \log c\\ &\log y=a \cos ^{-1} x\\ &\frac{1}{y} \frac{d y}{d x}=a \times\left(\frac{-1}{\sqrt{1-x^{2}}}\right)\\ &\frac{d y}{d x}=\frac{a y}{\sqrt{1-x^{2}}} \end{aligned}

        \begin{aligned} &\text { Squaring both sides, }\\ &\left(\frac{d y}{d x}\right)^{2}=\frac{a^{2} y^{2}}{\left(1-x^{2}\right)}\\ &\left(1-x^{2}\right)\left(\frac{d y}{d x}\right)^{2}=a^{2} y^{2} \end{aligned}

        \begin{aligned} &\text { Again differentiate, }\\ &\left(\frac{d y}{d x}\right)^{2}(-2 x)+\left(1-x^{2}\right) \times 2 \frac{d y}{d x} \frac{d^{2} y}{d x^{2}}=a^{2} \cdot 2 y \cdot \frac{d y}{d x}\\ &-x \frac{d y}{d x}+\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}=a^{2} y\\ &\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-a^{2} y=0 \end{aligned}

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2027 LIVE: Class 10, 12 exam dates announcement soon at cbse.gov.in, sample papers out
anam-khan

CBSE Board Exams 2027: LOC submission for Classes 10, 12 begins tomorrow; check dates and fees
anam-khan

CBSE Date Sheet 2027 LIVE: Class 10, 12 exam dates soon; LOC submission begins, guidelines

Latest Question