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

What is the inverse of y = x+3/4 ? a. y=x-3/4 b. y=4x-3 c. y=4x+3 d. y= x-3/-4

viva [34]

Y = x + 3/4

x = y - 3/4

swap the variables:-

y = x - 3/4 (answer). Its a.

4 0

3 years ago

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Now consider the expression 4.0×103+4×102. determine the values of a and k when the value of this expression is written in scien

natta225 [31]

Let`s say that the expression is written in the form:a * 10^k.4 * 10^3 + 4 * 10^2 = = 4 * 10 * 10^2 + 4 * 10^2 = = 40 * 10^2 + 4 * 10^2 = = 44 * 10^2 = 4.4 * 10^3.Answer:a = 4.4 and k = 3 and the expression in the scientific notation is:4.4 * 10^3.

6 0

3 years ago

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Which statement is true about the solution ?

Harrizon [31]

Answer:

There are no real solutions to this equation

Step-by-step explanation:

4 0

3 years ago