Advanced Math Archive: Questions from August 05, 2022
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\[ \int_{0}^{1} \int_{0}^{y} f(x, y) d x d y=\int_{0}^{1} \int_{0}^{x} f(x, y) d y d x \] True False3 answers -
Solve the following DEs: a. \( \mathrm{y}^{\prime \prime}+4 \mathrm{y}^{\prime}+13 \mathrm{y}=(4 t-4) \cos (3 t)+(12 t-6) \sin (3 t) \) b. \( \mathrm{y}^{\prime \prime}+4 \mathrm{y}^{\prime}+4 \mathrm1 answer -
1 answer
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1. Differentiate the following functions with respect to \( x \) : (a) \( y=\frac{4}{\sqrt{x}} \) [2] (d) \( y=3 x^{4}+3 x^{3}-9 x^{2}-3 x+13 \) [2] (b) \( y=\frac{1}{9 x^{4}} \) [2] (e) \( y=\left(51 answer -
(a) Find: \[ L^{-1}\left\{\frac{s e^{-s}}{s^{2}-4 s+13}\right\} \] (b) \[ L\left\{t e^{-2 t} \sin 5 t\right\} \]1 answer -
Solve the Cauchy-Euler IVP \[ x^{2} y^{\prime \prime}+3 x y^{\prime}+y=0 ; \quad y(1)=3 \quad y^{\prime}(1)=4 \]1 answer -
3 answers
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3 answers
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1 answer
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\( \iint_{R} \frac{9\left(1+x^{2}\right)}{1+y^{2}} d A, R=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq 1\} \)1 answer