Question
अवकल समीकरण :
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को प्राचल विचरण विधि से हल कीजिए।
Answer :
Word Count : 117
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_____ ______ _____ ____ _______ _______ ______ __________ __________ _______.
______ _____ _____ _______ _______ ___ _____ ______.
___ ____ ____ ____ _____ _____ ______ _________.
__________ ______ _________ _________ __________.
_____ ____ ____ ________ ____ ______.
______ ______ _____ ___ _________ _______.
___ _________ _______ ________ ____ ____.
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दिया हुआ अवकल समीकरण है (y''+6y'+9y=\dfrac{1}{x^3}e^{-3x}, ; x>0) सबसे पहले समजात समीकरण हल करते हैं (y''+6y'+9y=0) इसका सहायक समीकरण है (m^2+6m+9=0 \Rightarrow (m+3)^2=0) अतः मूल (m=-3,-3) हैं और समजात हल (y_c=(C_1+C_2 x)e^{-3x}) अब प्राचल विचरण विधि अपनाते हैं। यहाँ (y_1=e^{-3x}, ; y_2=xe^{-3x}) Wronskian [ W=\begin{vmatrix} y_1
________ ______ _______ _____ ______ ___ _________ ________ ____ ________._________ ______ ______ _____ _________ ______ ___ _______ ____ _________ _____ _______.
_____ ______ _____ ____ _______ _______ ______ __________ __________ _______.
______ _____ _____ _______ _______ ___ _____ ______.
___ ____ ____ ____ _____ _____ ______ _________.
__________ ______ _________ _________ __________.
_____ ____ ____ ________ ____ ______.
______ ______ _____ ___ _________ _______.
___ _________ _______ ________ ____ ____.
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