# MAT 330 Final Exam-.docx - MAT 330 Final ExamAssignment...

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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.
dy dx = 2 y d dx ( C e 2 x ) = 2 ( Ce 2 x ) C d dx ( e 2 x ) = 2 C e 2 x C ( 2 e 2 x ) = 2 C e 2 x 2 C e 2 x = 2 Ce 2 x Thus the solution is verified 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. )
y ( μ ( x ) )= Q ( x ) μ ( x ) dx Input values yx = xsinxdx sinxdx ( dx dx ) ¿ dx ¿ ¿ sinx dx ¿ yx = x ¿ yx =− xcosx + si nx + C ;C isanarbitrary constant y = 1 x (− xcosx + sin x + C ) y =− cosx + ( sinx ) x + C x ¿ To verify solution Take y =− cosx + ( sinx ) x + C x ¿ And differentiate y =− cosx + ( sinx ) x + C x ¿ y + cosx ( sinx ) x = C x x ( y + cosx ( sinx ) x )= C xy + xcosx sinx = C 1 y + x ( dy dx ) + 1 cosx + x ( sinx ) cosx = 0 y + x ( dy dx ) + cosx xsinx cosx = 0 x ( dy dx ) + y = xsinx Which equals original differential equation
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. y