JEE Mains · Maths · STD 12 - 9. differential equations
Let \( y=y(x) \) be the solution of the differential equation \( secx\frac{dy}{dx}-2y=2+3~sin~x, x\in(-\frac{\pi}{2},\frac{\pi}{2}), \) \( y(0)=-\frac{7}{4}. \) Then \( y(\frac{\pi}{6}) \) is equal to :
- A \( -\frac{5}{2} \)
- B \( -\frac{5}{4} \)
- C \( -3\sqrt{3}-7 \)
- D \( -3\sqrt{2}-7 \)
Answer & Solution
Correct Answer
(A) \( -\frac{5}{2} \)
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx}-2y~cos~x=2~cos~x+3~sin~x.cos~x \) \( I.F.=e^{-2~sin~x} \) \( e^{-2~sin~x}.y=\int e^{-2~sin~x}(3~sin~x~cos~x+2~cos~x)dx \) \( y.e^{-2~sin~x}=e^{-2~sin~x}(-\frac{3}{2}sin~x-\frac{7}{4})+C \) \( y=-\frac{3}{2}sin~x-\frac{7}{4}+C.e^{2~sin~x} \)…
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