Solve the initial value problem 2yy' + 2 = y² + 2x with y(0) = 8.a. To solve this, we should use the substitutionuWith this substitution,y =y'=help (formulas)help (formulas)help (formulas)dyEnter derivatives using prime notation (e.g., you would enter y' for).b. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'.help (equations)c. The solution to the original initial value problem is described by the following equation in x, y.help (equations)

Answered: Solve the initial value problem 2yy' +…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…
Solve the initial value problem 2yy + 5 = y + 5x with y(0) = 6. To solve this, we should use the substitution u = y^2 help (formulas) With this substitution, y = sqrtu help (formulas) y : 2ydy help (formulas) Enter derivatives using prime notation (e.g., you would enter y for ). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. help (equations) The solution to the original initial value problem is described by the following equation in x, y. у^2--5х+36е6х help (equations)
Solve the following differential equation xinx y' + y= 2lnx Select one: O a. F(x,y) = ylnx- (nx}? = c O b. YG.S Inx - (2(nx)? + c) O . F(x,y) = ylnx -2(Inx)? = c O d. None e. YG.s Inx -(Inx)² + c)
Write the particular solution of the first order linear differential equation (1 + x)dy + (y - cosx)dx 0; when y(0) = 1. In writing your final answer, follow the format 2x^3ycosx-3y^2+x^3y=c. If it involved product of a variable and trigonometric function, write first the variable followed by the trigonometric function. If in a term it involved x and y, write x first followed by y whatever the exponent be. The value of the constant of integration c is written on the right side of the equation. Strictly no spaces between symbols. Do not use grouping symbols for the product or multiplication symbol. All letters should be in small letter and the order of the addends is not necessary. Use the symbol (^) caret to denote the exponent of the variable. Use the / symbol to denote quotient. =
Solutions to the differential equation = xy also satisfy = y'(1+ 3x?y²). Let y = S(x) be a particular solution to the differential equation dx 3 xy with f(1) 2. (a) Write an equation for the line tangent to the graph of y = f(x) at x = 1. (b) Use the tangent line equation from part (a) to approximate f(1.1). Given that f(x) > 0 for 1 < x <1.1, is the approximation for f(1.1) greater than or less than f(1.1)? Explain your reasoning.

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