অবকলন সমীকরণ x2 dy + y2 dx = 0 এর সাধারণ সমাধান কী?

যেখানে c সমাকল ধ্রুবক

  1. x + y = c
  2. xy = c
  3. c(x + y) = xy
  4. উপরের কোনোটিই নয়

Answer (Detailed Solution Below)

Option 3 : c(x + y) = xy
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Detailed Solution

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অনুসৃত ধারণা:

গণনা:

প্রদত্ত:

x2dy + y2 dx = 0

⇒ x2dy = -y2dx

উভয় পক্ষকে সমাকলন করে, আমরা পাই

এখানে c হল অবকলন ধ্রুবক, ধরে নিন -c = 1/c (কারণ 1/cও একটি ধ্রুবক)

⇒ c(x + y) = xy

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