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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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Since, population of species A is represented by : P=2^{x} +19

Let us find the population of species A, at the end of week 1:

i.e., x = 1

i.e., P(1)=2^{1} +19

i.e., P(1)=2 +19

i.e., P(1)=21


Also, since population of species B is represented by : P=3^{x} +18

Let us find the population of species B, at the end of week 1:

i.e., x = 1

i.e., P(1)=3^{1} +18

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3 years ago
Pls answer<br><br> Y’all are awesome thx
Vilka [71]

Answer: 12a.) slope is 125, y-intercept is 50 (started at 50 ft)

12b.) f(3) = 425 feet

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Step-by-step explanation:

12a.) The slope equation is y = mx+b, where m is the slope, and b is the y intercept.

12b.) to find f(3) you could either plug it into the equation given (125x+50) or pretend there is a vertical line at 3 on the x axis, and where it crosses the line given would be the answer.

12c.) He is climbing a 500 ft cliff, and according to the graph, it takes him 3.6 hours to do it. Another way to find this answer would be to find f(3.6), which is indeed 500 ft.

Hope this helps!

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3 years ago
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salantis [7]

Answer:

x=

2

−5−

57

​

​

=−6.275

x=

2

−5+

57

​

​

=1.275

Step-by-step explanation:

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