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Jenis kestabilan solusi kesetimbangan tak nol dari persamaan diferensial $y'=\\var{a}y^2-(b-\\var{a})y^3$ adalah bukan stabil lokal.

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Nilai $b$ terkecil yang mungkin adalah $\\ldots$.

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Diketahui masalah nilai awal $(\\var{a}x+\\var{b}) \\,dy=(\\var{c}y+\\var{d})\\ln(\\var{c}y+\\var{d})\\,dx$ dengan $y\\left(\\simplify{({b}-1)/{a}}\\right)=\\frac{e-\\var{d}}{\\var{c}}$.

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Nilai dari $\\var{a}\\ln(\\ln(\\var{c}y+\\var{d}))+\\dfrac{\\var{c}}{\\ln(\\var{a}x+\\var{b})}$ adalah $\\ldots$.

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Diberikan model interaksi dua spesies $\\begin{cases} \\frac{dp}{dt} &= -\\var{a}p-\\var{b}pq+\\var{c}p^2 \\\\ \\frac{dq}{dt}&=\\var{c}q-\\var{d}pq+\\var{a}q^2 \\end{cases}$.

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Pernyataan berikut yang benar adalah $\\ldots$.

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Diberikan sistem persamaan diferensial $\\begin{cases}\\frac{dy}{dt}&=\\simplify{{a}{c}*x^2-({a}{d}+{b}{c})*x*y+{c}{d}*y^2}\\\\\\frac{dx}{dt}&=\\simplify{{b}/{a}-x}\\end{cases}$ untuk $x(t)\\geq 0$ dan $y(t)\\geq 0$.

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Pernyataan yang benar terkait model tersebut adalah $\\ldots$.

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$y$-nullcline pada model tersebut adalah $y=\\simplify{{d}/{c}}$.

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Misalkan $N(t)$ menyatakan banyaknya suatu populasi pada saat $t$. Populasi berevolusi menurut persamaan logistik dengan pengaruh pemangsa sehingga laju pertumbuhannya dapat dimodelkan sebagai $\\displaystyle\\frac{dN}{dt}=\\left(N^2-N\\right)\\left(1-\\frac{N}{\\var{b}}\\right)-\\frac{\\var{a}N^2-\\var{a}N}{\\var{b}+N}$.

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Misal $\\hat N = \\hat N_1$, $\\hat N = \\hat N_2$, dan $\\hat N = \\hat N_3$ menyatakan seluruh titik kesetimbangan model tersebut. Maka $\\hat N_1 + \\hat N_2 + \\hat N_3 = \\ldots$.

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Solusi kesetimbangan bersifat stabil lokal di $\\hat{N}=\\ldots$.

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Solusi kesetimbangan bersifat tidak stabil di $\\hat{N}=\\ldots$.

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Jenis kestabilan solusi kesetimbangan tidak dapat disimpulkan di $\\hat{N}=\\ldots$.

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Waktunya 5 menit lagi ya.

Selamat datang!

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Petunjuk pengerjaan soal:

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• Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
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• Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \$$\\frac{2}{3}\$$.
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• Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik 2/3 untuk menjawab \$$\\frac{2}{3}\$$.
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Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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