Mathematics, 13.06.2020 08:57 angelrenee2000

The variables x and y satisfy the differential equation dy/dx= xe^x+y. It is given that y = 0 when x = 0. (i) Solve the differential equation, obtaining y in terms of x.

(ii) Explain why x can only take values that are less than 1.

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Answer from: GingerSnaps

Rewrite the ODE

$\dfrac{\mathrm dy}{\mathrm dx}=xe^x+y$

$\dfrac{\mathrm dy}{\mathrm dx}-y=xe^x$

Divide both sides by e^x :

$e^{-x}\dfrac{\mathrm dy}{\mathrm dx}-e^{-x}y=x$

The left side condenses to the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dx}\left[e^{-x}y\right]=x$

Integrate both sides and solve for :

$e^{-x}y=\displaystyle\int x\,\mathrm dx=\frac12x^2+C$

$y=\dfrac12x^2e^x+Ce^x$

Given that y=0 when x=0 , we find

$0=\dfrac120^2e^0+Ce^0\implies C=0$

so that the solution is

$\boxed{y(x)=\dfrac{x^2e^x}2}$

I'm not sure I understand the claim that must be less than 1...

Answer from: Quest

This polygon has 4 sides
180(4-2) = 180(2) = 360 degree
80+90+2x + 3x = 360
170+5x = 360
5x = 190
x= 38
measure of angle t is 2(38)= 76
the answer is c. trust me
hope this !

Answer from: Quest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

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