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

2 years ago

Choose the equation that best represents the general form of the following expression. x^2/2=7x user: what is the value of "c" i

AlexFokin [52]

X^2/2 = 7x
x^2 = 14x
x^2 - 14x = 0

A quadratic equation is of the form ax^2 + bx + c
Therefore, in 3x^2 + 5x + 7, c = 7

4 0

2 years ago

You cut off half of a strip of paper.Then you cut off half of the piece that is left.Then you cut off half of the remaining piec

7nadin3 [17]

It goes like this 1/2, 1/4, 1/8. But if your asking about what fraction didn’t get affected than that just zero because the original peace was cut in half.

If that’s not what you mean can you please elaborate to me!

7 0

2 years ago

Help me with this :))))

Crank

Answer:

answer is 11.9...... have a good day

6 0

2 years ago

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