Mathematics, 16.03.2020 07:48, yoooo9313

What is the solution to the differential equation dydx=5y2 with the initial condition y(0) = 3?

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answered: abby2572

Step-by-step explanation:

$dydx = 5y^{2} \\\frac{dy}{5y^{2}} = dx\\$

Integrating both sides yields:

$-\frac{1}{5y} = x + c\\ y = -\frac{1}{5x + 5c} \\y(0) = 3 = 3 = -\frac{1}{0 + 5c} = c = -\frac{1}{15}$

Our solution is:

$y = -\frac{1}{5x - \frac{1}{3} }$

answered: lexipeacemaker

Differential equation is a way to represents the relation between the functions and their variables.The solution to the differential equation given in the question is,

$y=\dfrac{3}{15x-1}$

Given-

The equation in the question is,

${dy\times {dx}=5y^2$

What is differential equation?

Differential equation is a way to represents the relation between the functions and their variables.

Rewrite the equation,

$\dfrac{dy}{5y^2} =dx$

Integration both sides,

$-\dfrac{1}{5y} =x+c$

Here c is the integrating constant.

Now the given initial condition is,

y(0)=3

Use this for the integrated function to find the value of the constant,

$-\dfrac{1}{5\times 3} =c$

$c=-\dfrac{1}{15}$

Put this value in equation we get,

$-\dfrac{1}{5y} =x-\dfrac{1}{15}$

$y=\dfrac{3}{15x-1}$

Hence the solution to the differential equation given in the question is,

$y=\dfrac{3}{15x-1}$

For more about the differential equation follow the link below-

answered: Guest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

answered: Guest

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!