JEE Mains · Maths · STD 12 - 9. differential equations
Let \( y=y(x) \) be the solution of the differential equation \( x^{4}dy + (4x^{3}y + 2\sin x)dx = 0 \), \( x>0 \), \( y(\frac{\pi}{2})=0 \). Then \( \pi^{4}y(\frac{\pi}{3}) \) is equal to:
- A 81
- B 92
- C 64
- D 72
Answer & Solution
Correct Answer
(A) 81
Step-by-step Solution
Detailed explanation
\( (x^{4}dy+4x^{3}ydx) = -2\sin x dx \) \( \Rightarrow \int d(x^{4}y) = \int -2\sin x dx \) \( \Rightarrow x^{4}y = 2\cos x + c \) \(\Rightarrow x^4 f(x)=2 \cos x+c\) As \(f\left(\frac{\pi}{2}\right)=0\) So, \(c =0\)…
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