Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 23

Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 23

Answers (1)

Answer:

Proved

Hint:

You must know about the derivative of exponential function

Given:

y=e^{2x}(ax+b), \: \: show\: \: that\: \: y_{2}-4y_{1}+4y=0

Solution:

y=e^{2x}(ax+b)\; \; \; \; \; \; \; \; \; ......(1)

        \begin{aligned} &\text { By using product rule of derivation }\\ &\frac{d y}{d x}=e^{2 x} \frac{d y}{d x}(a x+b)+(a x+b) \frac{d}{d x} e^{2 x} \\ &\frac{d y}{d x}=a e^{2 x}+2(a x+b) e^{2 x}\\ &\frac{d y}{d x}=e^{2 x}(a+2 a x+2 b) \end{aligned}.....(2)

        \begin{aligned} &\text { Again differentiating both sides w.r.t } x, \text { using product rule }\\ &\frac{d^{2} y}{d x^{2}}=e^{2 x} \frac{d y}{d x}(a+2 a x+2 b)+(a+2 a x+2 b) \frac{d}{d x} e^{2 x}\\ &\frac{d^{2} y}{d x^{2}}=2 e^{2 x}+2(a+2 a x+2 b) e^{2 x} \quad \ldots .(3) \end{aligned}

        In\; order\; to\; prove\; the\; expression\; try\; to\; get\; the\; required\; f\! orm \\Subtracting\; 4 \times equation\; (2)\; f\! rom\; equation (3)\\ \frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}=2 e^{2 x}+2(a+2 a x+2 b) e^{2 x}-4 e^{2 x}(a+2 a x+2 b)\\ \frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}=2 a e^{2 x}-2 e^{2 x}(a+2 a x+2 b)\\ \frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}=-4 e^{2 x}(a x+b)

        \begin{aligned} &\text { Using equation }(1)\\ &\frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}=-4 y\\ &\frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}+4 y=0\\ &y_{2}-4 y_{1}+4 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 Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question