We saw that every autonomous rstorder differential equation dy/dx = f (y) is separable. Does this fact
Question:
We saw that every autonomous rstorder differential equation dy/dx = f (y) is separable. Does this fact help in the solution of the initial-value problem
Dy/dx = √(1+ y2) sin2 y, y(0) = ½ ?
Discuss. Sketch, by hand, a plausible solution curve of the problem.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (2 reviews)
Separating variables we have dy 1 y 2 sin 2 y dx ...View the full answer
Answered By
Vineet Kumar Yadav
I am a biotech engineer and cleared jee exam 2 times and also i am a math tutor. topper comunity , chegg India, vedantu doubt expert( solving doubt for iit jee student on the online doubt solving app in live chat with student)
5.00+
2+ Reviews
10+ Question Solved
Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
Question Posted:
Students also viewed these Mathematics questions
-
The autonomous differential equation with x(0) = l. This describes a population with per capita production that decreases like 1/1 + x 2 . Describe in words how the solution differs from that in...
-
Consider the autonomous rst-order differential equation dy/dx = y 2 - y 4 and the initial condition y(0) = y 0 . By hand, sketch the graph of a typical solution y(x) when y0 has the given values. (a)...
-
Consider the autonomous first-order differential equation dy/dx = y - y 3 and the initial condition y(0) = y 0 . By hand, sketch the graph of a typical solution y(x) when y 0 has the given values....
-
George operates a business that generated adjusted gross income of $250,000 and taxable income of $170,000 this year (before the domestic production activities deduction). Included in income was...
-
See the T accounts below. The equipment was sold for a gain of $5,000. Using this infor- mation, indicate the items to be reported on the statement of cash flows using the direct method. Accumulated...
-
Name the three data properties that an IS must have.
-
Give the formula for calculating sample size. Define each part of the formula.
-
Roger R. and Michelle N. Stewart (ages 45 and 46) are married and live at 641 Cody Way, Casper, WY 82609. Roger is a consulting engineer, and Michelle is a paralegal. They file a joint return and use...
-
A shallow trench for a 1000 feet waterline installation willtake ten days. It will take four days to install the first 400 feetof pipe. A water meter will then be installed during the followingtwo...
-
Reading Readiness, Inc. has provided you its list of accounts and balances as of January 31. The Controller has asked you to prepare an Income Statement for the month ended January 31. Use the...
-
A one-parameter family of solutions of the first-order differential equation dy/dx = xy 1/2 is y = (1/4 x 4 + c) 2 for c 0. Each solution in this family is dened on (-, ). The last statement is not...
-
(a) Solve the two initial-value problems: Dy/dx = y, y(0) = 1 and dy/dx = y + y/x ln x, y(e) = 1. (b) Show that there are more than 1.65 million digits in the y-coordinate of the point of...
-
Complete the "Julia's Food Booth" case problem on page 109 of the text. Address each of the issues A - D according the instructions given. (A) Formulate and solve an L.P. model for this case. (B)...
-
4. Assume the following two MIPS codes are given to you. Answer the following questions based on the assumptions that values of 10, 20, 30, and 40 are assigned to registers $30, $s1, $s2, $s3, and...
-
Converting Binary to 8421 BCD 1. Convert 111011010 to BCD 2. Convert 111011111 to BCD 3. Convert 10001000 to BCD 4. Convert 1101 to BCD 5. Convert 11110011 to BCD Convert Binary to 4221 BCD 6....
-
3. T (n) is defined recursively as 1 T(n) = { 2. [ 2 =1 if n = 1, otherwise. T(i) What is the order of T(n)? In other words, find an expression f(n) such that T(n) = 0(f(n)). You now implement the...
-
2. Convert the following C code to appropriate MIPS assembly. You will turn this in on paper (typed or handwritten), but you are encouraged to test in SPIM. int i= 0; while (i < 5) { printf("Loop...
-
Please label the direction of the drift and diffusion (electrical) currents for both electrons and holes, given their carrier concentration distribution profiles and the applied electric field marked...
-
Our dependency on fossil fuels has many repercussionsboth economic and environmental. For example, the 2010 explosion of BPs Gulf of Mexico oil rig is, to date, the largest accidental oil spill in...
-
2. In the circuit given in Figure 2, i,(t) = 5.67cos(5t)A and v (t) = 70.71 cos(5t 60) V a) Find the equivalent load impedance. State whether the load is inductive or capacitive. b) Calculate the...
-
(a) Show that the general solution of Is Where A = c 2 1 + c 2 2 and the phase angles and are, respectively, defined by sin = c 1 /A, cos = c 2 /A and b) The solution in part (a) has the form...
-
Consider a driven undamped spring/mass system described by the initial-value problem
-
Find the charge on the capacitor in an LRC-series circuit at t = 0.01 s when L = 0.05 h, R = 2, C = 0.01 f, E(t) = 0 V, q(0) = 5 C, and i(0) = 0 A. Determine the first time at which the charge on the...
-
In what ways does HR assist managers in handling employee performance issues or conflicts within their teams? What role does HR play in helping managers navigate challenges related to allegations and...
-
Why is A/B testing so useful for marketing, and digital marketing in particular? Give at least two examples of A/B testing for marketing purposes. Give a null and alternative hypothesis for one of...
-
Define the following sets (30 points) (a) X = {(x, y) = R: y = f(x) = 3x + 3y 42} =1 (b) Y={(x, y) = R: y = f(x) = 2x + 2y 42} (c) Z = XUY (d) Prove whether or not each set defined above is convex?
Study smarter with the SolutionInn App