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cluponka [151]
3 years ago
9

First-order linear differential equations

Mathematics
1 answer:
garik1379 [7]3 years ago
4 0

Answer:

(a) \frac{dy}{(2y+1)}=tdt (b) y=\frac{e^{t^2}+e^{2c}-1}{2}

Step-by-step explanation:

(1) We have given \frac{dy}{dt}+ycost=0

\frac{dy}{dt}=-ycost

\frac{dy}{y}=-costdt

Integrating both side

lny=-sint+c

y=e^{-sint}+e^{-c}

(2) \frac{dy}{dt}-2ty=t

\frac{dy}{dt}=2ty+t

\frac{dy}{dt}=t(2y+1)

\frac{dy}{(2y+1)}=tdt

On integrating both side  

\frac{ln(2y+1)}{2}=\frac{t^2}{2}+c

ln(2y+1)={t^2}+2c

2y+1=e^{t^2}+e^{2c}

y=\frac{e^{t^2}+e^{2c}-1}{2}

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3 years ago
bob has 64 cups. could he distribute them into 6 equally in stacks and not have any left over? Explain
Iteru [2.4K]

Bob cannot distribute the cups in six equal stacks and not have any left over.

Step-by-step explanation:

In order to divide the total number of cups in six equal stacks with no left over, the total number of cups will be divided by 6, if there is any remainder then the cups cannot be equally divided with no left over.

So

Dividing 64 by 6

= \frac{64}{6} \\= 10\frac{4}{6}

Here

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As there are 4 cups left, Bob cannot distribute the cups in six equal stacks and not have any left over.

Keywords: Division, fractions

Learn more about division at:

  • brainly.com/question/4464845
  • brainly.com/question/4522984

#LearnwithBrainly

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3 years ago
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neonofarm [45]

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Hope this help!

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