Existence-Uniqueness Theorem: If f(x, y) and df/dy are continuous on a rectangle R in the xy-plane containing the initial condition y(x0)=y0, then the initial value problem y’=f(x,y), y(x0)=y0 has a unique solution in R. 6pts Determine whether the Existence-Uniqueness Theorem can be used to determine if the initial value problem: y’ = 1/x + y1/3,    (1,1)  has a unique solution.  Please indicate the largest possible rectangle R from the Theorem.   21pts First order ODEs: Solve the following. Provide solutions in explicit form if possible. Theorem: M(x,y) dx + N(x,y) dy = 0 is an exact equation if dM/dy = dN/dx. a.  (y4 + 1)cos x dx – y3 dy = 0 b.  (12x – y)dx – 3x dy = 0 c.  (x3 + y/x)dx + (y2 + ln x) dy = 0   8pts Homogeneous ODE: Solve y iv + 5y ‘’ – 36y = 0.   10pts Nonhomogeneous ODEs: Solve the following with either undetermined coefficients or variation of parameters to solve  3y ‘’ – y’ – 2y = 4x + 1, y(0) = 1 and y’(0) = 0   10pts Systems: Solve the following.                   x1’ = 2×1 – 4×2                                      x2’ = 2×1 – 2×2   15pts Solve the initial value problem for y(t) using the method of Laplace transforms. y ’’ + 4y’ + 3y = 1 y(0)=0,   y’(0) = 0   Taylor polynomial about 0: pn(x) = f(0) + f’(0)x + f ‘’(0)/2! x2 + f ‘’’(0)/3! x3 +  … + f (n)(0)/n! xn   15pts Determine the first three nonzero terms in the Taylor polynomial approximations for the given initial value problem y ’’ – 2y’ + y = 0;          y(0)=0,   y’(0) = 1   Theorem: Consider the differential equation A(x) y” + B(x) y’ + C(x) y = 0.  If the functions p(x) = B(x)/A(x) and q(x) = C(x)/A(x) are analytic at x =0, then the general solution is produced by the power series centered at x=0: y(x) = a0 + a1x + a2 x2 + a3 x3 + …   15pts Determine the first four nonzero terms in the power series expansion about x=0 for a general solution in the given ODE y ’’ + xy’ + y = 0           

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Dystocia is largely due to

What is the outermost part of a tooth’s crown called?

An occupational therapist closely examines the steps a client must perform to load clothes into a washing machine.The therapist notes specific physical and cognitive actions such as: Bending down to pick up the laundry basket Gripping and lifting the basket with both hands Maintaining balance while carrying the basket across the room Opening the washing machine door using fine motor skills Selecting the correct wash cycle by turning a knob with appropriate hand strength and motor planning The therapist is focused on breaking down the specific motor and process skills required for each step. This type of analysis is BEST described as ________. 

True or False: Section GG scoring is a factor in the determination of payment in post-acute settings such as Inpatient Rehabilitation Facilities and Skilled Nursing Facilities.

An occupational therapist conducts a satisfaction survey to evaluate the quality of OT services in an outpatient program. The questionnaire developed by the therapist asks respondents to rate their responses to quality statements according to a 4-point Likert scale of agreement. Which statement best reflects an accurate measure of satisfaction? 

Code 06 – Independent – The patient completes the activity by him/herself without any assistance from a helper. Code 05 – Setup or clean-up assistance:  The patient completes the activity and a helper assists prior to or following the activity but not during the activity. Code 04 – Supervision or touching assistance:  The patient completes the activity, but a helper has to supervise the patient, provide verbal cues, or provide touching assistance, steadying assistance or contact guard assistance. Code 03 – Partial/Moderate assistance:  The patient completes the activity with the assistance of a helper who provides less than half of the effort. Code 02 – Substantial/Maximal assistance:  The patient completes the activity with the assistance of a helper who provides more than half of the effort. Code 01 – Dependent:  The patient provides none of the effort to complete the activity or needs two or more helpers to complete the activity. For the following question, please use the Section GG codes above. Tina requires a helper to retrieve her socks and shoes. She puts on both socks and both shoes without any assistance. What is Tina’s GG code?

Consider the levels of measurement learned in this course (nominal, ordinal, interval, and ratio). In the Activity Card Sort clients sort pictures into categories to identify their level of performance in ADLs/IADLs. Which of the following best identifies the level of measurement used in this assessment?

Read the following statement and determine which section of the SOAP note it belongs in.  “Inability to incorporate breathing techniques and energy conservation techniques into basic ADL tasks without verbal prompts limits her ability to live alone independently after discharge.”