Question

Give the alternative corresponding to the solution of the equation y' = 5y : x - 5y = c. ln⁡|x| + y = c. 5x - ln⁡|y| = c. x - ln⁡|1/y| = c.

163

likes
814 views

Answer to a math question Give the alternative corresponding to the solution of the equation y' = 5y : x - 5y = c. ln⁡|x| + y = c. 5x - ln⁡|y| = c. x - ln⁡|1/y| = c.

Expert avatar
Birdie
4.5
100 Answers
Step-by-step solution:

1. Start with the differential equation y' = 5y .

2. This is a first-order linear differential equation that can be solved by separation of variables.

3. Rearrange the equation: \frac{dy}{y} = 5 dx .

4. Integrate both sides:

\int \frac{1}{y} dy = \int 5 dx

\ln|y| = 5x + C

5. Solve for y :

y = e^{5x + C} = Ce^{5x}

6. Rewrite the constant term to match the alternative forms:

\ln|y| = 5x + \ln|C|

7. Recognize that \ln|C| can be absorbed by a constant term, so:

5x - \ln|y| = C \quad \text{or} \quad \ln|y| = 5x + C'

The corresponding form is:

5x - \ln|y| = c .

Frequently asked questions (FAQs)
Math question: Calculate the standard deviation of a dataset containing [10, 15, 20, 25, 30]?
+
Math question: What is 3/4 of 80 when expressed as a decimal?
+
Math question: Simplify √125 - √32
+
New questions in Mathematics
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that
1. Suppose we have a good whose quantity supplied changed from 100 to 120 units when the price increased from $10 to $12 per unit. Compute the price elasticity of supply using the midpoint method
9b^2-6b-5
A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?
The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
4. Show that if n is any integer, then n^2 3n 5 is an odd integer
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?
3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.
The following table shows the frequency of care for some animal species in a center specializing in veterinary dentistry. Species % Dog 52.8 Cat 19.2 Chinchilla 14.4 Marmoset 6.2 Consider that the center only serves 10 animals per week. For a given week, what is the probability that at least two are not dogs? ATTENTION: Provide the answer to exactly FOUR decimal places
A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
9.25=2pi r solve for r
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.
2x-5-x+2=5x-11
The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the x−axis is
Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?
The domain of the function f(x)=x+7x2−144 is (−∞,), ( ,), and ( , ∞).