First slide

Methods of solving first order first degree differential equations

Question

$If y = y (x) satisfies the differential equation 8 \sqrt{x} (\sqrt{9 + \sqrt{x}}) dy = (\sqrt{4 + \sqrt{9 + \sqrt{x}}})^{- 1} dx$ , $x > 0 and y (0) = \sqrt{7} then y (256) =$

Difficult

A

3
B

9
C

16
D

80

Solution

$dy= \frac{dx}{(8 \sqrt{x} \sqrt{9+ \sqrt{x}}) \sqrt{4+ \sqrt{9+ \sqrt{x}}}}$
$\begin{array}{l} Let 4 + \sqrt{9 + \sqrt{x}} = t \\ \Rightarrow \frac{1}{2 \sqrt{9 + \sqrt{x}}} \cdot \frac{1}{2 \sqrt{x}} d x = d t \\ ∴ d y = \frac{d t}{2 \sqrt{t}} \end{array}$
Integrating on both sides
$y = \sqrt{t} + c = \sqrt{4 + \sqrt{9 + \sqrt{x}}} + c$
$p u t x = 0, y (0) = \sqrt{7}$
$\sqrt{7} = \sqrt{4 + \sqrt{9 + 0}} + c c = 0$
$y (256) = \sqrt{4 + \sqrt{9 + \sqrt{256}}} = \sqrt{4 + \sqrt{9 + 16}} = \sqrt{4 + 5} = 3$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App