Solution manual of mathematic

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Solution manual of mathematic

CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main pinpose of Section 1.1 IS simply to intro

Solution manual of mathematicoduce the basic notation and terminology of differential equations, and to show the student what is meant by a solution of a differential equation. Al

so, the use of differential equations in the mathematical modeling of real-world phenomena is outlined.Problems 1-12 are routine verifications by dnec Solution manual of mathematic

t substitution of the suggested solutions into the given differential equations. We include here just some typical examples of such verifications.3If

Solution manual of mathematic

yt = cos2.V and y, = sin 2x, then )\ = - 2sin 2.V y2 = 2cos 2.V. soy\ = -4 cos 2.V = -4y, and y2 = -4 sin 2x = -4y,. Thus y\ + 4y, = 0 and y*+4y, = 0.

CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main pinpose of Section 1.1 IS simply to intro

Solution manual of mathematic(

yf+4yi + 4y1 = (4 Solution manual of mathematic

2.V and y, = sin .V - cos 2.V. then y[ = - sin -V+2 sin 2.V.y\ = - cos -V + 4 cos 2.V. y2 = cos .V + 2 sin 2x. and y* = - sin .V + 4 cos 2.V. HenceT1

Solution manual of mathematic

*+T1 = (-cos.v + 4cos2x) + (cos.v-cos2.v) = 3cos2.vandy* + y, = (-sui.v + 4cos2.v) + (smx-cos2x) = 3cos2.v.1Copyright ệ 2015 Pearson Education, Inc2 D

CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main pinpose of Section 1.1 IS simply to intro

Solution manual of mathematic0.If y = y, = x"2 In X. then y' = X-3 - 2 x"3 bì X and y" = - 5 x“* + 6 x“ bì X, sox:y* + 5xy' + 4y = X2 (-5X*4 + 6x“* lnx) + 5x(x"3 -2x"3 lnx) + 4(x"

2 hlx)= (-5x'2+5x"2) + (6x-2-10x'2+4x’2)lnx = 0.13Substitution of y = en into 3y' = 2y gives the equation 3r en = 2ea, which simplifies to 3r = 2. Thu Solution manual of mathematic

s r = 2/3.14Substitution of y = en into 4y* = y gives the equation 4r2 en = e*. which simplifies to 4r: = 1. Thus r = ±1/2.15Substitution of y = en in

Solution manual of mathematic

to y' +y- 2y = 0 gives the equation t'e* + /•/*- 2ea = 0. which simplifies to r2 + r - 2 = (r + 2)(r -1) = 0. Thus r = -2 or r = 1.16Substitution of y

CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main pinpose of Section 1.1 IS simply to intro

Solution manual of mathematic solutionsr = (-3±T57)/6.The verifications of the suggested solutions in Problems 17-26 are similar to those in Problems 1-12. We illustrate the deter

mination of the value of c only in some typical cases. However, we illustrate typical solution curves for each of these problems.17c = 218. c = 3Copyr Solution manual of mathematic

ight €■ 2015 Pearson Education. Inc.

CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main pinpose of Section 1.1 IS simply to intro