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Differential Equations: An Introduction to Modern Methods and Applications
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- Question 7 Eliminate the arbltrary constant of y= GX+ Czexarrow_forwardSolve. Find the equation of a line normal to the curve of y-cos COS at x=1. 2 Select one: A. -3.3 x + 9y - 9 + /3 n = 0 B. -3,3 x + 3y + 3/3 - = 0 C. -6/3 x + 3y - Gu/3 - i = 0 D. 3 x + 3y - 3- 1= 0arrow_forwardHelp with parts a through e, having some difficulty with the phase lines.arrow_forward
- The distances between Earth and nearby planets can be approximated using the phase angle α, as shown in the figure. Suppose that the distance between Earth and the sun is 93,000,000 miles and the distance between Venus and the sun is 67,000,000 miles. Approximate the distance between Earth and Venus to the nearest million miles when α = 34.arrow_forwardThe equation of a curve is y=x+2 cos x. Find the x co-ordinates of the stationary points of the curve for 0 < x< 2m, and determine the nature of each of these stationary points.arrow_forwardKk.425. Sketch the time dependent solutions based on the on-dimensional phase line of:arrow_forward
- 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tut 80x + 1000x = 2500 cos where r = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of time t (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (a) Find the general solution to this nonhomogeneous ODE. Note that your answer will have a term in it which is a function of v.arrow_forwardClassify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos x=0 b. 8ty"-6t²y'+4ty-3t²-0 c. sin(x²)y"-(cosx)y'+x²y = y'-3 d. y"+5xy'-3y = cosy 2. Verify using the principle of Superposition that the following pairs of functions y₁(x) and y2(x) are solutions to the corresponding differential equation. a. e-2x and e-3x y" + 5y' +6y=0 3. Determine whether the following pairs of functions are linearly dependent or linearly independent. a. fi(x) = ex and f(x) = 3e³x b. fi(x) ex and f2 (x) = 3e* 4. If y(x)=e³x and y2(x)=xe³x are solutions to y" - 6y' +9y = 0, what is the general solution? Question 1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos…arrow_forwardIn each of Problems 7 through 12, find the solution of the given initial value problem. Draw the trajectory of the solution in the ₁2-plane and also draw the component plots of ₁ versus t and of x2 versus t.arrow_forward
- Solve the following equation: y''+4y'+7y=0arrow_forwardQuestion 4: Linearize i + 2i + 2x? - 12x + 10 = 0. Around its equilibrium positionarrow_forwardIn a 24-hour period, the water depth in a harbour changes from a minimum of 3/2 m at 2 am to a maximum of 7 at 8:00 am. Which of the following equations best describes the relationship between the depth of the water and time in the 24-hour time period? ³ (π (t− 2)) + ¹/7 d=-c COS (t− 2)) + ¹/7 d = −sin (π (t− 2)) + d= cos (π (t-2 1/ π d = sin (π (t− 2)) + 24/7arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage