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...
-
What is a data attribute (or field)?
-
It is desired to find the value f0.99 for an F10,5 distribution. Use Table A.5 and the F5,10 distribution to find this value. Table A.5 Critical Values for the F Distribution Area Denominator Degrees...
-
Gallop, Inc. is a toy manufacturer specializing in games for boys and girls aged eight to twelve. On March 30, Gallop had predicted first-quarter earnings of $.20 per share. On April 15, Gallop...
-
Monica Gellar owns a famous restaurant called Famous Kitchen. During a busy night at the restaurant, a spark went off in the kitchen and caused a fire. The restaurant had to immediately shut down....
-
Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year, and nearly 80% of the college and universities without open admissions policies use SAT scores in...
-
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...
-
According to Figure 1, within the protein ARKKKK60491, which of the following locations contain polypeptide N-termini? I. Position A II. Position B III. Position C (A) I only (B) I and II (C) II and...
-
Reprographics Ltd. manufactures a document-reproducing machine which has a variable cost structure as follows: Sales during the current year are expected to be 13,50,000 and fixed overheads,...
-
ABC Ltd. manufactures cakes in three varietiesA, B, and Ceach requiring similar material, labour, and production facilities. The trading results of the firm for current year ending March are as...
-
Royal Industries Ltd. is considering the replacement of one of its moulding machines. The existing machine is in good operating condition but is smaller than required if the firm is to expand its...
-
Michael Vaughn is preparing his balance sheet and income and expense statement for the year ending June 30, 2010. He is having difficulty classifying six items and asks for your help. Which, if any,...
-
Jonathan Lansing, a 47-year-old retail store manager earning $75,000 a year, has worked for the same company during his entire 28-year career. A major economic recession has caused massive layoffs...
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If f' is continuous on [1, 3], then Sf(e) dv...
-
On July 1, 2011, Flashlight Corporation sold equipment it had recently purchased to an unaffiliated company for $480,000. The equipment had a book value on Flashlights books of $390,000 and a...
-
(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...
-
Generate a Development Plan for the Bike-sharing Kiosks system project along with a change control Control management identify how the change will occur. For example: Who is responsible for managing...
-
How do central banks use open market operations to influence liquidity in the financial system, and what impact does this have on interest rates and inflation?
-
If you were reviewing a dissertation or article, what would you look for in the introduction? What would make you want to continue reading? Are there one or two items in your introduction that you...
Study smarter with the SolutionInn App