JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y = y(x)\) be the solution of the differential equation \((\tan x)^{1/2}\,dy = (\sec^3 x - (\tan x)^{3/2} y)\,dx\), \(0 < x < \dfrac{\pi}{2}\), \(y\left(\dfrac{\pi}{4}\right) = \dfrac{6\sqrt{2}}{5}\). If \(y\left(\dfrac{\pi}{3}\right) = \dfrac{4}{5}\alpha\), then \(\alpha^4\) equals _______.
- A 48
- B 50
- C 54
- D 58
Answer & Solution
Correct Answer
(A) 48
Step-by-step Solution
Detailed explanation
The given differential equation can be rewritten as: \(\dfrac{dy}{dx} + (\tan x)y = \dfrac{\sec^3 x}{(\tan x)^{1/2}}\) This is a linear differential equation of the form \(\dfrac{dy}{dx} + P(x)y = Q(x)\). Integrating Factor (IF) =…
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