Question
अनिर्धारित गुणांक विधि से अवकल समीकरण :$
को हल कीजिए। (4)
Answer :
Word Count : 438
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दी गई अवकल समीकरण है: [ (D^3 + 2D^2 - D - 2)y = e^x + x^2 ] चरण 1: सममित अवकल समीकरण का हल (समान्य हल) समान्य हल के लिए अवकल समीकरण का गुणांक समीकरण लें: [ D^3 + 2D^2 - D - 2 = 0 ] साझा कारक समूह करें: [ (D^3 + 2D^2) - (D + 2) = D^2(D + 2) - 1(D + 2) = (D^2 - 1)(D + 2) ] [ (D - 1)(D + 1)(D + 2) = 0 ] अतः समान्य हल है: [ y_h = C_1 e^x + C_2 e^{-x} + C_3 e^{-2x} ] चरण 2: विशेष हल (अनिर्धारित गुणांक विधि) दाएँ ओर है (e^x + x^2) 1. (e^x) के लिए: चूंकि (D - 1 = 0) पहले से समान्य हल में है
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