Question

प्राचल विचरण विधि से निम्नलिखित अवकल समीकरण: equation को हल कीजिए। equation 

09 Jan 2026
Answer :
Word Count : 361
दी गई अवकल समीकरण है: [ y'' - 2y' + y = \frac{12 e^x}{x^3}. ] सबसे पहले, इसका समांतर (homogeneous) समीकरण देखें: [ y'' - 2y' + y = 0. ] समान्य हल के लिए चरित्र समीकरण है: [ r^2 - 2r + 1 = 0 \implies (r-1)^2 = 0 \implies r = 1 \text{ (दोहराव) }. ] इसलिए समान्य ___ ______ ________ ____ ____ ______ _______ _______ ________ _______ ____.
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