be quick please 4. For the following equation which of the following is correct? * (8...
For the following equation which of the following is correct? (8 Puan) (ye + 2x)dx + (xe" - 2y)dy = 0 exact, nonlinear and separable linear, not exact and not separable exact, nonlinear and not separable nonlinear, not exact and not separable linear, separable but not exact exact linear but not separable nonlinear, separable but not exact exact linear and separable
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8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. * (8 Puan) y (4) - 9y" = 5 + e* (x – 3) +e3x + 4 sin(3x). none of these O Ar? + Bxe3x + Cet + Dxet + Esin(3x) + F cos(3x) O AX + B + C sin (3x) + D cos(3x) + Exet O A + Be-3x + CxeBr + Det + Exel +...
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10. Find all singular points of the following equation and determine whether each one is regular or irregular?* (8 Puan) x? (1 - x)?y" + 2xy' + 4y = 0 0 0 and 1 are regular singular points. 0 0 and 1 are irregular singular points. Onone of these 1 is a regular singular point, O is an irregular singular point. O O is a regular singular point, 1 is an irregular singular point.
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2. Solve the following initial value problem * (8 Puan) = 8x2e-2y, y(0) = 1 dx O y = 1 In(4x4 + f2) O y = In(2x - 1) O y = -48x²e-2y O y = In(4x4 – 3) O y = {In(2x' + e?) O none of these O y = In(4x4 + 5) O y = 2x4 + e-2y+2 O y = In (2x + e)
Question 8: [20 marks] a) Determine the type of the differential equation+3)xy+(x* +6x +9)cosx (is +9 coSx (15S it linear/ nonlinear, separable/non-separable, homogeneous/non-homogeneous)? b) Find the particular solution subject to the initial condition y(0) 6.
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE: (b) Use your classification from (a) to use an appropriate method in the following problem. Be sure to clearly label steps to maximize your score Find an explicit solution of +y=sin(x). Explicit Solution: (c) Give the largest interval over which the general solution is defined. (d) Are there any transient terms in the general solution? If yes, what are they?
8-11: Determine if the following problem is a separable or a linear differential equation or neither, then solve the first-order differential equation.If it is an initial value problem, find the exact solution. dy .dr a2y-ycos y(0) 3 8. 9. e(y-)da+ (1 + e*dy) = 0 10. (cos r)y (sin )y 1, y(T) = 1 shared via du dr 3yx-2a2- x with y(1) 0 11. a 12. In 1980 the population of alligators estimated to be 1500. In 2006 the population...
Which of the following is true for the first order nonlinear ODES? O All first order nonlinear ODEs are separable. O All first order nonlinear ODEs are either separable or exact. O It is possible that a first order nonlinear ODE is neither separable nor exact. O All first order nonlinear ODEs are exact.
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone (3x+3x - 3y)dx + (xy? - x-2)dy = 0 Select all that apply. A. has an integrating factor p(x) or p(y) not equal to a constant OB. linear OC. separable D. exact E. none of the above
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone. (4x+3x - 3y)dx + (xy3 – x-2)dy = 0 Select all that apply. A. exact B. has an integrating factor u(x) or (y) not equal to a constant C. linear D. separable E. none of the above