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मान लें कि k एक धनात्मक पूर्णांक है। निम्न अवकलन समीकरण पर विचार करें

\(\left\{\begin{aligned} \frac{d y}{d t} &=y^{\frac{5 k}{5 k+2}} \text { for } t>0, \\ y(0) &=0 \end{aligned}\right.\)

निम्न कथनों में से कौन-सा सच है?

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. इसका अद्वितीय हल हैं जो (0, ∞) पर संतत: अवकलनीय है
  2. इसके अधिकतम दो हल हैं जो (0, ∞) पर संतत: अवकलनीय है
  3. इसके अनंतत: बहु हल हैं जो (0, ∞) पर संतत: अवकलनीय है
  4. इसका (0, ∞) पर कोई संतत: अवकलनीय हल नहीं है

Answer (Detailed Solution Below)

Option 3 : इसके अनंतत: बहु हल हैं जो (0, ∞) पर संतत: अवकलनीय है
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Q3.मान लें कि k एक धनात्मक पूर्णांक है। निम्न अवकलन समीकरण पर विचार करें \(\left\{\begin{aligned} \frac{d y}{d t} &=y^{\frac{5 k}{5 k+2}} \text { for } t>0, \\ y(0) &=0 \end{aligned}\right.\) निम्न कथनों में से कौन-सा सच है?

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