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-BARSIC- [3]
2 years ago
12

The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Mathematics
1 answer:
Sav [38]2 years ago
4 0

Replace y' with \dfrac{\mathrm dy}{\mathrm dx} to see that this ODE is separable:

2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}

Integrate both sides; on the left, set u=y^2+4 so that \mathrm du=2y\,\mathrm dy; on the right, set v=\ln x so that \mathrm dv=\dfrac{\mathrm dx}x. Then

\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v

\implies\ln|u|=\ln|v|+C

\implies\ln(y^2+4)=\ln|\ln x|+C

\implies y^2+4=e^{\ln|\ln x|+C}

\implies y^2=C|\ln x|-4

\implies y=\pm\sqrt{C|\ln x|-4}

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Answer:

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4 0
2 years ago
Help me show work please<br>​
GREYUIT [131]
Angle 4 would also be 135. the two on the top would add to 180, making a whole circle altogether that equals 360. so, you would do 180-135 = 45. angle 5 is 45. angle 7 would also be 135 because angle 4 and 7 are vertical angles.
5 0
3 years ago
Find the compound interest on 30,000 for 2years at 7 percent per annum​
hjlf

Answer:

34347

Step-by-step explanation:

Use the formula s=p(1+r/k)^kt

p=30000

r=7% (interest)

k=1 (because of per annum)

t= 2 (years)

Hence: 30000(1+0.07/1)^1(2) = 34347

7 0
2 years ago
Joel has a goal to practice is clarinet for 4 1/2 hours per week the list below shows the number of hours Chihuahuas practice so
Natasha_Volkova [10]

Complete question:

Joel has a goal to practice his clarinet for 4 1/2 per week. The list below shows the number of hours Joel has a practiced so far for the week. Monday 1 1/2 hours Wednesday 1 1/4 hours Thursday 1 hour How many more hours does he need to practice this week to meet his goal

Answer: 3/4 hours

Step-by-step explanation:

Target hours = 4 1/2 hours = 9/2 hours

Number of hours so far :

(1 1/2 + 1 1/4 + 1) = (3/2 + 5/4 + 1) hours

Total so far :

L. C. M of denominator = 4

(6 + 5 + 4) /4 = 15/4

Number of hours left to meet his target equals :

Target hours - total so far

( 9/2 - 15/4)

L. C. M of denominator = 4

(18 - 15) / 4 = 3/4 hours

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7 0
3 years ago
Last night, Christina received 4 messages from Kyle, 11 from Christina, 5 from Steven, 9 from Kevin, and 24 from Natalie. What i
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This = P(message is from Steven) =  number of messages from steven / total number of messages  from previous night

=  5 / (4+11+5+9+24) =   5/53 Answer
7 0
3 years ago
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