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Diberikan persamaan integral-diferensial

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$\\displaystyle y'(t)+\\var{a*b}\\int_0^t y(s)\\, ds=\\var{a*b^2}t\\var{a+b}y(t).$

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Persamaan ini dapat diubah menjadi persamaan diferensial orde dua $y''+ay'+by=c$ dengan cara menurunkan kedua ruas terhadap variabel $t$. Diperoleh nilai $a$, $b$, dan $c$ berturut-turut adalah $\\ldots$.

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Solusi umum dari persamaan diferensial tersebut adalah $y(t)=C_1e^{\\lambda_1 t}+C_2e^{\\lambda_2 t}+D$ dengan $\\lambda_1<\\lambda_2$. Diperoleh nilai $\\lambda_1$, $\\lambda_2$, dan $D$ berturut-turut adalah $\\ldots$.

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Jika $y(0)=\\var{b}$ dan $y'(0)=\\var{a}$, maka nilai $C_1$ dan $C_2$ berturut-turut adalah $\\ldots$.

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$\\displaystyle \\lim\\limits_{t\\to\\infty}\\dfrac{y(t)}{e^t}=\\ldots$.

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