Word Count : 368

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दी गई प्रारंभिक मान समस्या है: [ y'' - 3y' + 2y = 6e^{-t}, \quad y(0) = 3, \quad y'(0) = 3 ] सबसे पहले हम लाप्लास रूपांतरण लागू करते हैं। याद रखें कि [ \mathcal{L}{y'(t)} = sY(s) - y(0), \quad \mathcal{L}{y''(t)} = s^2 Y(s) - s y(0) - y'(0) ] जहाँ (Y(s) = \mathcal{L}{y(t)}) है। चरण 1: लाप्लास रूपांतरण [ _____ _____ ______ ________ _________ ______ ___ ___ ___.
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