Solve 4xy' — 20y = x¯¹, given y(1) = −3. First, identify the integrating factor, r(x). r(x) = ☐ help (formulas) Now find the general solution. y(x) = ☐ help (formulas) Note: Use C for the arbitrary constant. Finally, solve the initial value problem y(1) = −3. y(x) = ☐ help (formulas) Book: Section 1.4 of Notes on Diffy Qs

* Salue the equation:- (2x -44+5)y'=x- 2y+3

+ I/ MI * 00 Energy consumption in a particular country in quadrillion BTUS can be modeled by C(x) = - 0.014x + 1.295x+ 68,958, where x is the number of years after 1970. a. One solution to the equation 89.258 = - 0.014x+ 1.295x+68.958 is x = 20. What does this mean? b. Graphically verify that x 20 is a solution to 89.258 = - 0.014x+1.295x + 68.958. c. To find when after 2020 the energy consumption in that country will be 89.258 quadrillion BTUS according to the model, is there a need to find the second solution to this equation? Why or why not? a. Choose the correct answer below. O A. In 1990, consumption was 68.958 quadrillion BTUS. O B. In 2020, consumption was 68.958 quadrillion BTUS. O C. In 1990, consumption was 89.258 quadrillion BTUS. O D. In 2020, consumption was 89.258 quadrillion BTUS. Click to select your answer and then click Check Answer. parts 2. remaining Clear All Check Answer P Pearson &17 PM ere to search 近 1202/LL/Z PrtSc F11 F12 F10 sup F7 F8 & Backspace 23 3. i 5.…

Differentiate. 4) f(x) = e2x 5) y = e6x2, x

solve ar + b 35. 2; for x Cx + d - 2[b – 3(c – x)] = 6; for x 37. a'x + (a – 1) = (a + 1)x; for x

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A virus is believed to be spreading through a sheep farm according to that equation N = 450 (11 + 249e−0.1t ) where N is the number of sheep infected and t is the number of days.(i) How many sheep are infected at t = 0?(ii) Using a spreadsheet calculate the number of sheep infected after 0, 10, 30 , 50, 70, 100 days)(iii) Will all the sheep become infected eventually? Give reasons to support your answer

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Solve for the general solution (Dª – 16)y = x* + x + 1

By using fixed points find the roots of equation f(x) = x + 4x – 2 x, = 0 E= 0. .0001