JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x\) such that \(\mathrm{y}(0)=\frac{5}{4}\). Then \(12\left(\mathrm{y}\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)\) is equal to _______.
- A 20
- B 21
- C 22
- D 23
Answer & Solution
Correct Answer
(B) 21
Step-by-step Solution
Detailed explanation
\(\text {I.F. } =\mathrm{e}^{\int 2 \sec ^2 x d x} \) \( =\mathrm{e}^{2 \tan x}\) Solution of diff. eq. \(y \cdot e^{2 \tan x}=\int e^{2 \tan x}\left(2 \sec ^2 x+3 \tan x \cdot \sec ^2 x\right) d x \)…
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