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zvonat [6]
2 years ago
7

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0​

Mathematics
1 answer:
dmitriy555 [2]2 years ago
8 0

Multiply the original DE by xy:

xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)

Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes

x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0

This final equation is easily recognized as separable:

dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides

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simplify: f(x)=3x²-6x-7
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Find the inverse function of y=1
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To find the inverse, interchange the variables and solve for y

f^−1(x)=−7x+7

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The next model of a sports car will cost 4.7% more than the current model. The current model costs $48,000. How much will the pr
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increase - $2256

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multiply the percent (in decimal form) by the original cost

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The largest z-score available in most tables is 2.99, which corresponds to a probability of 99.86%. A fair coin is
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Answer:

The number of heads observed is 121.14 heads

Step-by-step explanation:

The formula for the z-score of a proportion is given as follows;

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{pq}{n}}}

Where:

{\hat{p} = Sample proportion

p = Population success proportion = 0.5

q = 1 - p = 1 - 0.5 = 0.5

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Hence, we have;

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∴ The number of heads observed = 200 × 0.6057 = 121.14 heads.

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2 years ago
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