AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(y+\cos x\left(\frac{d y}{d x}\right)-\cos ^2 x=0\) is
- A \((\sec x+\tan x) y=x+\cos x+c\)
- B \((1+\cos x) y=(x+c) \cos x-\cos ^2 x\)
- C \((1+\sin x) y=(x+c) \cos x-\cos ^2 x\)
- D \((\sec x+\tan x) y=x-\sin x+c\)
Answer & Solution
Correct Answer
(C) \((1+\sin x) y=(x+c) \cos x-\cos ^2 x\)
Step-by-step Solution
Detailed explanation
\(\cos x \frac{dy}{dx} + y = \cos^2 x\) \(\frac{dy}{dx} + (\sec x)y = \cos x\) \(IF = e^{\int \sec x dx} = e^{\ln|\sec x + \tan x|} = \sec x + \tan x\) \(y(\sec x + \tan x) = \int (\cos x (\sec x + \tan x)) dx + C\) \(y(\sec x + \tan x) = \int (1 + \sin x) dx + C\)…
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