Given the differential equation

$5t^3 \frac{dx}{dt} +2x-2=0$

The solution is as follows:

$5t^3 \frac{dx}{dt} +2x-2=0 \\ \\ \Rightarrow5t^3 \frac{dx}{dt} =2-2x \\ \\ \Rightarrow \frac{5}{2-2x} dx= \frac{1}{t^3} dt \\ \\ \Rightarrow \int {\frac{5}{2-2x} } \, dx = \int {\frac{1}{t^3}} \, dt \\ \\ \Rightarrow- \frac{5}{2} \ln(2-2x)=- \frac{1}{2t^2} +A \\ \\ \Rightarrow\ln(2-2x)= \frac{1}{5t^2} +B\\ \\ \Rightarrow2-2x=Ce^{\frac{1}{5t^2}} \\ \\ \Rightarrow 2x=Ce^{\frac{1}{5t^2}}+2 \\ \\ \Rightarrow x=De^{\frac{1}{5t^2}}+1$

3 0

3 years ago

Adam is 9 years old and Billy is 11 years old. What will be the ratio of Adams’ age to Billy’s age in exactly one year’s time? G

son4ous [18]

Answer:

10 / 12

simplified:

5/6

since 5 is a prime number, we can't simplify this ratio any further

4 0

3 years ago

Will give brainliest mark plz helpp urgenttt easyy

Finger [1]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

- 4x + 3y = 12 ( add 4x to both sides )

3y = 4x + 12 ( divide the terms by 3 )

y = $\frac{4}{3}$ x + 4 ← in slope- intercept form

with slope m = $\frac{4}{3}$ and y- intercept c = 4

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Given

- 5x + 3y = - 9 ( add 5x to both sides )

3y = 5x - 9 ( divide the terms by 3 )

y = $\frac{5}{3}$ x - 3 ← in slope- intercept form

with slope m = $\frac{5}{3}$ and y- intercept c = - 3

8 0

3 years ago