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rosijanka [135]
3 years ago
14

Solve the initial value problem yy′+x=x2+y2‾‾‾‾‾‾‾√ with y(1)=8‾√. To solve this, we should use the substitution u= x^2+y^2 help

(formulas) u′= 2x+2yy' help (formulas) Enter derivatives using prime notation (e.g., you would enter y′ for dydx). After the substitution from the previous part, we obtain the following linear differential equation in x,u,u′.
Mathematics
1 answer:
leva [86]3 years ago
7 0

Looks like the equation is

yy'+x=\sqrt{x^2+y^2}

Substitute u(x)=x^2+y(x)^2, so that u'=2x+2yy'. Then the equation is the same as

\dfrac{u'-2x}2+x=\sqrt u\implies u'=2\sqrt u\implies\dfrac{\mathrm du}{2\sqrt u}=\mathrm dx

Integrate both sides to get

\sqrt u=C\implies\sqrt{x^2+y^2}=C

Given that y(1)=\sqrt8, we have

\sqrt{1^2+(\sqrt8)^2}=C\implies C=3

so the solution is

\sqrt{x^2+y^2}=3

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What is the fully factored form of 32a^3 + 12a^2?
Klio2033 [76]

<u>Answer:</u>

4a^{2} (8a + 3)

<u>Step-by-step explanation:</u>

32a^3 + 12a^2

To factorize this, start by taking the common variable out. As we have two powers for the same variable a, we can take the smaller power of a as a common to get like shown below:

32a^3 + 12a^2

a^2 (32a + 12)

Now when you have taken the variable as a common, try and take out a common number from the coefficient of a as well:

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So, the fully factored form of 32a^3 + 12a^2 is 4a^2 (8a + 3).

7 0
3 years ago
There are 28.35 g in an ounce and 2.21 lb in a kilogram. Juanita converts 3 kilograms to ounces. Is her conversion correct? Expl
GarryVolchara [31]

Answer:

3 kg = 105.82 ounces

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1 ounce = 28.35 g

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1 kg = 2.21 lb

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1 kg = 35.274 ounces

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4 0
3 years ago
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