Word Count : 370

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दिया गया समीकरण है: \[ y'' - 10y' + 9y = 5x, \quad y(0) = -1, \quad y'(0) = 2 \] इस समीकरण को लाप्लास रूपांतर का उपयोग करके हल करेंगे। ### 1. लाप्लास रूपांतर लागू करना: समीकरण में \( y'' \), \( y' \), और \( y \) के लिए लाप्लास रूपांतर ज्ञात होते हैं: \[ \mathcal{L}\{y''\} = s^2 Y(s) - s y(0) - y'(0) \] \[ \mathcal{L}\{y'\} = s Y(s) - y(0) \] \[ \mathcal{L}\{y\} = Y(s) \] यहाँ \( Y(s) \) लाप्लास रूपांतर है \( y(t) \) का, और ________ _________ _________ ___ ____ ____ _______.
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