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- Suppose solving an equation by Laplace transform results in 6 s Y(s) = s2 + 64° Evaluate y(r).arrow_forwardFigure 1.5.8 shows a slope field and typical solution curves for the equation . (a) Show that every solution curve approaches the straight line y= -x - 1 as x goes to negative infinity. (b) For each of the five values y sub1 = -10, -5, 0, 5, and 10, determine the initial value (accurate to five decimal places) such that y(5) = y sub1for the solution satisfying the initial condition y(-5) = y sub0. Image: Slope field and solution curves for y' = x + yarrow_forwardAsaparrow_forward
- 1. A park ranger watches a scavenging falcon soaring above a lake. Suppose the position of the bird relative to the ranger is modelled by the path r(t), where t is measured in seconds and the components of †(t) are measured in meters. 7(0) Suppose the bird is initially at rest and that the initial position of the bird (15, 15, 10) and that the bird's acceleration is à(t) = (10 cos t, 20 sin t, 0) = Find 7(1) - the position of the falcon after 1 second elapses.arrow_forwardQuestion 2. Solve the following initial value problem (DO NOT use Laplace transform method): +y-4- 4y=3e-4-6 x=// 10=0 70=2arrow_forwardProblem 2: Use the Laplace transform to solve y'+ 2y =U(t – 3), y(0) = 0.arrow_forward
- answer number 5 asapp for 30 minutesarrow_forwardPart 2. Consider an ODE of the form x²y" + axy' + by = 0 with given constants a and b and unknown solution y(x). Assuming that y(x) follows the form y = xm, perform the following tasks: 2A. Solve for y'(x) and y" (x) and transform the given ODE in terms of x, m, a, and b. 2B. Determine the characteristic equation of the ODE. For each solution listed below, determine the corresponding roots of the characteristic equation and derive the respective Cauchy-Euler ODE: -3 2C. y = x ³ +1 2D. y = (1 + Inx)x` 2E. y = x[cos(2lnx) + sin(2lnx)]arrow_forward1. A spring with a mass of 2 kg requires a force of 6N to stretch the spring 0.5m beyond its natural length. There is a damping force that is directly proportional to 14 times the instantaneous velocity. Initially, the spring is stretched 1m be- low equilibrium and released from rest. Use Laplace Transforms to find the equation of motion for the mass on the spring at any time t.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education