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Download Solution PDFअवधारणा:
फॉर्म की प्रारंभिक मान समस्या का संख्यात्मक हल उत्पन्न करने के लिए यूलर की विधि:
y' = f (x, y), y(x0) = y0
yn + 1 = yn + h f(xn, yn)
गणना:
हमारे पास है,
x0 = 0, y0 = 1 , h = 0.1
x1 = x0 + h
n = 0 के लिए
⇒ y1 = y0 + hf(xn, yn)
⇒ y1 = 1 - 0.1 × (0 - 1)2
⇒ y1 = 1 - 0.1
⇒ y1 = 0. 9
n = 1 के लिए
⇒ y2 = y1 + hf(x1 - y12)
⇒ y2 = 0.9 + 0.1[0.1 - (0.9)2]
⇒ y2 = 0.9 + 0.1[0.1 - 0. 81]
⇒ y2 = 0.9 - 0.1 × 0.71
⇒ y2 = 0.9 - 0.071
⇒ y2 = 0. 829
⇒ y2 = 0.83
∴ लगभग दो दशमलव स्थान मान 0.83 है
Last updated on Jul 18, 2025
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