Superfastjellyfish
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- Jan 3, 2015
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Questions 31 - 33: Consider the differential equation:
. . . . .\(\displaystyle y"\, -\, 3y'\, +\, 2y\, =\, \sin(x)\)
...with initial conditions \(\displaystyle \, y(0)\, =\, 1\, \) and \(\displaystyle \, y'(0)\, =\, 2.\,\) Find the maximal solution \(\displaystyle \,y\,\) of this problem and answer the following questions.
31. The value of \(\displaystyle \, 10\, y(\pi)\,\) is equal to:
a) \(\displaystyle 10\, +\, e\) . . .b) \(\displaystyle e^{\pi}\, \left(12e^{\pi}\, -\, 5\right)\, -\, 3\) . . .c) \(\displaystyle 3\, -\, 10\, \sin(\pi)\, +\, e^{2\pi}\) . . .d) \(\displaystyle \pi e^{-2 \pi}\, -\, 3\) . . .e) \(\displaystyle \dfrac{3}{4}\, -\, \dfrac{e^{\pi}}{4}\)
32. The solution \(\displaystyle \, y\, \) is on its domain:
a) decreasing . . .b) constant . . .c) \(\displaystyle 2 \pi\)-periodic . . .d) increasing . . .e) none of these
33. The limit \(\displaystyle \displaystyle{ \lim_{x\, \rightarrow \, +\infty} \,}\) \(\displaystyle \dfrac{y(x)}{e^{2x}}\,\) is equal to:
a) \(\displaystyle +\infty\) . . .b) \(\displaystyle \dfrac{3}{2}\) . . .c) \(\displaystyle 0\) . . .d) \(\displaystyle \dfrac{6}{5}\) . . .e) does not exist
Ive learned this stuff 7 years ago, if somebody can show me how it is done Id be so grateful !
. . . . .\(\displaystyle y"\, -\, 3y'\, +\, 2y\, =\, \sin(x)\)
...with initial conditions \(\displaystyle \, y(0)\, =\, 1\, \) and \(\displaystyle \, y'(0)\, =\, 2.\,\) Find the maximal solution \(\displaystyle \,y\,\) of this problem and answer the following questions.
31. The value of \(\displaystyle \, 10\, y(\pi)\,\) is equal to:
a) \(\displaystyle 10\, +\, e\) . . .b) \(\displaystyle e^{\pi}\, \left(12e^{\pi}\, -\, 5\right)\, -\, 3\) . . .c) \(\displaystyle 3\, -\, 10\, \sin(\pi)\, +\, e^{2\pi}\) . . .d) \(\displaystyle \pi e^{-2 \pi}\, -\, 3\) . . .e) \(\displaystyle \dfrac{3}{4}\, -\, \dfrac{e^{\pi}}{4}\)
32. The solution \(\displaystyle \, y\, \) is on its domain:
a) decreasing . . .b) constant . . .c) \(\displaystyle 2 \pi\)-periodic . . .d) increasing . . .e) none of these
33. The limit \(\displaystyle \displaystyle{ \lim_{x\, \rightarrow \, +\infty} \,}\) \(\displaystyle \dfrac{y(x)}{e^{2x}}\,\) is equal to:
a) \(\displaystyle +\infty\) . . .b) \(\displaystyle \dfrac{3}{2}\) . . .c) \(\displaystyle 0\) . . .d) \(\displaystyle \dfrac{6}{5}\) . . .e) does not exist
Ive learned this stuff 7 years ago, if somebody can show me how it is done Id be so grateful !
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