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BIRTEKLI EMES SÍZÍQLÍ DIFFERENCIALLÍQ TEŃLEMENIŃ ULÍWMA SHESHIMI
[eng: general solution of an inhomogeneous linear differential equation, рус: общее решение неоднородного линейного дифференциального уравнения]
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30.10.2024 13:56
BIRTEKLI EMES SÍZÍQLÍ DIFFERENCIALLÍQ TEŃLEMENIŃ ULÍWMA SHESHIMI [en: general solution of an inhomogeneous linear differential equation, ru: общее решение неоднородного линейного дифференциального уравнения]
– sáykes birtekli teńlemeniń ulıwma sheshimi menen berilgen birtekli emes teńlemeniń dara sheshiminıń qosındısına teń boladı. Mısalı: $\dfrac{d^{2}y}{dx^{2}} + 5y = 1$ birtekli emes teńlemesi $y_{1} = \dfrac{1}{5}$ dara sheshimine iye. Bul birtekli emes teńlemege sáykes keliwshi $\dfrac{d^{2}y}{dx^{2}} + 5y = 0$ birtekli teńlemeniń ulıwma sheshimi $y_{2} = C_{1}\sin\sqrt{5}x + C_{2}\cos\sqrt{5}x$. Sonda berilgen birtekli emes teńlemeniń ulıwma sheshimi tómendegishe boladı: $y = y_{1} + y_{2} = C_{1}\sin\sqrt{5}x + C_{2}\cos\sqrt{5}x + \dfrac{1}{5}$.