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Ivenika [448]
3 years ago
7

X dy/dx +2y =x^2logx by using Bernoulli's Equation

Mathematics
1 answer:
inna [77]3 years ago
3 0
This ODE isn't of Bernoulli type, but it is linear, so we should be able to find an integrating factor to solve it.

x\dfrac{\mathrm dy}{\mathrm dx}+2y=x^2\log x\implies\dfrac{\mathrm dy}{\mathrm dx}+\dfrac2xy=x\log x

The integrating factor will be

\mu(x)=\exp\left(\displaystyle\int\frac2x\,\mathrm dx\right)=x^2

Multiplying both sides of the ODE by the IF gives

x^2\dfrac{\mathrm dy}{\mathrm dx}+2xy=x^3\log x
\dfrac{\mathrm d}{\mathrm dx}[x^2y]=x^3\log x
x^2y=\displaystyle\int x^3\log x\,\mathrm dx

Integrate the right hand side by parts to get

x^2y=\dfrac14x^4\log x-\dfrac1{16}x^4+C
y=\dfrac14x^2\log x-\dfrac1{16}x^2+\dfrac C{x^2}
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7+(-3)+(-5)-10<br>how do i simplify ​
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Solve for brainlist :)
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Assume a simple random sample of 10 BMIs with a standard deviation of 1.186 is selected from a normally distributed population o
kirza4 [7]

Answer:

a) H0: \sigma = 1.34

H1: \sigma \neq 1.34

b) df = n-1= 10-1=9

And the critical values with \alpha/2=0.005 on each tail are:

\chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589

c) t=(10-1) [\frac{1.186}{1.34}]^2 =7.05

d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Step-by-step explanation:

Information provided

n = 10 sample size

s= 1.186 the sample deviation

\sigma_o =1.34 the value that we want to test

p_v represent the p value for the test

t represent the statistic  (chi square test)

\alpha=0.01 significance level

Part a

On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:

H0: \sigma = 1.34

H1: \sigma \neq 1.34

The statistic is given by:

t=(n-1) [\frac{s}{\sigma_o}]^2

Part b

The degrees of freedom are given by:

df = n-1= 10-1=9

And the critical values with \alpha/2=0.005 on each tail are:

\chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589

Part c

Replacing the info we got:

t=(10-1) [\frac{1.186}{1.34}]^2 =7.05

Part d

For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

5 0
2 years ago
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