MAT 330 Final Exam.docx - MAT 330 Final Exam Assignment...

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MAT 330 Final Exam Assignment Instructions: For each problem, be sure to show all steps for arriving at your solution. Work within this document. Use an equation tool as needed, and submit everything in one file. 1. For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution. y
2. For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution.
x [ y + cos sinx x ] = C Distribute x: xy + xcosx sinx = C Differentiate x: 1 × y + dy dx + 1 ×cosx + ( sinx ) cosx = 0 Simplify: y + x dy dx + cosx xsinx cosx = 0 x dy dx + y = xsinx The general solution can be transformed into the differential equation. Therefore, x dy dx + y = xsinx is a solution for x dy dx + y = xsin ( x ) 3. For the below ordinary differential equation with initial conditions, state the order and determine if the equation is linear or nonlinear. Then find the solution of the ordinary differential equation, and apply the initial conditions. Verify your solution.
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