Consider the differential equation y 3 y' 9x 2 = 0. (a) Write it as y

Question:

Consider the differential equation y³y' − 9x²= 0.

(a) Write it as y dy = 9x dx. (b) Integrate both sides to obtain y4 = 3x + C. (c) Verify that y = (12x + C)/4

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 22, 2023 04:44 AM

See More Questions

Given the schedule and time for completion of a project: Immediately Preceding Hours needed to perform the task Task 1 2 3 4 5 6 7 8 9 1 1 2 2,3 4 2,3 4,5 6,7,8 Tasks 9 7 4 5 7 3 2 4 6 (1) Draw PERT...
Consider the differential equation dP/dt = f (P), where f (P) = 20.5P 3 - 1.7P + 3.4. The function f (P) has one real zero, as shown in the following figure. Without attempting to solve the...
Myklebust Corporation's relevant range of activity is 4,000 units to 8,000 units. When it produces and sells 6,000 units, its average costs per unit are as follows: Direct materials Direct labor...
Research an organization that has EITHER done a great job at identifying how they are socially responsible, or that has gotten into "hot water" for not being ethical in their advertising. If you...
Draw the shear and moment diagrams for thebeam. 10 kN 2 kN/m
Suppose that a family has four children, and each child is equally likely to be a boy or a girl. a. Write out the sample space of 16 possible outcomes. (For example, use the notation B1G2G3B4 to mean...
You run at $4 \mathrm{~m} / \mathrm{s}$ in the same direction as a river flowing at $2 \mathrm{~m} / \mathrm{s}$. This speed is enough to keep you chatting with your friend who is steering a slow...
Carbon monoxide is burned with excess air at 1 atm in an adiabatic reactor. The reactants are fed at 25C and the final temperature (i.e., the adiabatic flame temperature) is 1400C. (a) Calculate the...
1. Consider two satellites S and S with periods of revolution 1hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S to the angular...
Solve the Initial Value Problem using Separation of Variables. xyy'= 1, y(3) = 2
A simpler model for the spread of a rumor assumes that the rate at which the rumor spreads is proportional (with factor k) to the fraction of the population that has not yet heard the rumor. (a)...
Determine the slope at A. EI is constant. C - L B Probs. 8-28/29 L- W
The ledger accounts of Dar Al Fatina show the following account balances as of March 31, 20X6. Prepare a trial balance for the company as of the same date. Accounts Payable Accounts Receivable Cash...
A ____________________, or person who agrees with the dissenting viewpoint, is likely to reduce conformity.
A person shown a picture and asked to make up a story about it would be taking a __________personality test.
According to Vygotsky, information that is within a childs __________ __________ __________ __________is most likely to result in cognitive development.
According to Freud, people use __________ __________as a means of preventing unwanted impulses from intruding on conscious thought.
When sales volume increases, which company will experience a larger percentage increase in profit: company X, which has mostly fixed expenses, or company Y, which has mostly variable expenses?
AB CORPORATION ISSUED THE FOLLOWING 850 COMMON STOCKS PAR VALUE P100 750 PARTICIPATING PREFERRED STOCKS PAR VALUE P100 AT 3% AB CORPORATION DECLARED P100,000.00 DIVIDEND IN 2022.
Evaluate the following limits or explain why they do not exist. Check your results by graphing. 1/x lim (ex + x)/ 0
Determine which of the two functions grows faster or state that they have comparable growth rates. ln x and log 10 x
a. Find the critical points of f on the given interval. b. Determine the absolute extreme values of f on the given interval. c. Use a graphing utility to confirm your conclusions. f(x) = x ln (x/5)...
Governor Asa Hutchinson announced that nurses in Arkansas would receive a $1,000 monthly bonus payment during the pandemic, and that number would double to $2,000 if they worked in a facility with a...
An investor believes that NVDA stock is a good purchase. She wants to believes that the stock will appreciate 8% following the next earnings call. Currently NVDA trades for $700/share. The investor...
The given function is not defined at a certain point. How should it be defined at that point to make it continuous at that point? f(x) = x+2x-80 x-8

Consider the differential equation y 3 y' 9x 2 = 0. (a) Write it as y

Question:

(a) Write it as y³ dy = 9x² dx. (b) Integrate both sides to obtain y4 = 3x³ + C. (c) Verify that y = (12x³ + C)¹/4 is the general solution. (d) Find the particular solution satisfying y(1) = 2.

Step by Step Answer:

Solving yy 9x 0 for y yields yy 9x a Separating variables in the last e...View the full answer

Calculus

Students also viewed these Mathematics questions