Explanation Procedure used: Consider the first order differential equation: M ( x , y ) d x + N ( x , y ) d y = 0 Find out M x and N y The condition for the exact differential is given by, M y = N x Where, M y is ∂ M ∂ y and N x is ∂ N ∂ x . Calculation: Consider the differential equation in the general form. ( cos x sin x − x y 2 ) d x + y ( 1 − x 2 ) d y = 0 (1) Compare and obtain, M ( x , y ) = ( cos x sin x − x y 2 ) (2) N ( x , y ) = y ( 1 − x 2 ) (3) Partially differentiate the equation (2) with respect to y . M y ( x , y ) = − 2 x y Partially differentiate the equation (3) with respect to x . N x ( x , y ) = − 2 x y Here, M y = N x therefore the equation (1) is exact. Integrate M ( x , y ) with respect to d x considering y as a constant and N ( x , y ) with respect to d y considering x as a constant from equation (1)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 2.4, Problem 41E

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To explain: The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at (−1, 1).

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Chapter 2.4, Problem 40E

Chapter 2.4, Problem 42E

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Fill in all the justifications to complete this formal proof, following all conventions from the textbook. 1. Ax~Q(x) 2. Ax(Q(x)vR(x)) 3. @n Premise Premise 4. | ~Q(n) 5. | Q(n)vR(n) 6. || Q(n) 7. || # 8. || R(n) 9. || R(n) 10. | R(n) 11. AxR(x)

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1. Name the ongiewing) 2. Name five pairs of supple 3 27 and 19 form a angles 210 and 21 are complementary angies 4. m210=32 mal!= 5 mc11-72 m10= 6 m210-4x mc11=2x x= 7 m210=x m 11 =x+20; x= 12 and 213 are supplementary angles 8 ma 12 2y m13-3y-15 y= 9 m 12-y+10 m13-3y+ 10: y= 10. The measure of 212 is five times the measure of 13. Find the 213 and 214 are complementary angles, and 14 and 15 are supplementary angies 11 mc13 47 m/14- 12 m 14-78 m13- m215- m15 13 m15-135 m. 13- m.14

Chapter 2 Solutions

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The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at ( − 1 , 1 ) .

Solution Summary: The author explains the definition of the explicit solution of IVP at (-1,1).

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To explain: The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at (−1, 1).

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Chapter 2 Solutions