Word Count : 269

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दी गई दो-आवर्ती समीकरण है: [ \frac{d^2 x}{dt^2} - 3 \frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0 ] यह एक रैखिक समकालीन (linear homogeneous) द्विघात अवकल समीकरण है। सबसे पहले इसके लिए चर हल मानते हैं: [ x(t) = e^{rt} ] इसे समीकरण में रखते हैं: [ r^2 e^{rt} - 3 r e^{rt} - 10 e^{rt} = 0 \implies r^2 - _________ ______ _____ __________ ____ ________ ___ _____.
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