Word Count : 288

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हमारे पास द्विघात रैखिक अवकल समीकरण है: [ \frac{d^2 y}{dx^2} - 2 \frac{dy}{dx} + 10 y = 0, ] साथ ही प्रारंभिक स्थितियाँ: [ y(0) = 4, \quad \frac{dy}{dx}(0) = 1. ] सबसे पहले, इस अवकल समीकरण के लिए सहसमाधान (complementary solution) ढूँढते हैं। मान लेते हैं कि [ y = e^{rx}. ] इसे समीकरण में प्रतिस्थापित करें: [ r^2 e^{rx} - 2 r e^{rx} + 10 e^{rx} = 0 \implies r^2 _______ _______ _____ _________ _______ _______ ____ ______ _____ ________ __________.
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