AP EAMCET · Maths · Differential Equations
The solution of the differential equation \(\frac{d y}{d x}-y \tan x=e^x \sec x\) is
- A \(y=e^x \cos x+c\)
- B \(y \cos x=e^x+c\)
- C \(y=e^x \sin x+c\)
- D \(y \sin x=e^x+c\)
Answer & Solution
Correct Answer
(B) \(y \cos x=e^x+c\)
Step-by-step Solution
Detailed explanation
Given linear differential equation is \[ \begin{aligned} \frac{d y}{d x}-y \tan x & =e^x \sec x \\ \therefore \quad \quad \quad \mathrm{IF}=e^{\int-\tan x d x} & =e^{-\log \sec x} \\ & =\frac{1}{\sec x} \end{aligned} \] \(\therefore\) Complete solution is…
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