Solution manual of mathematic
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Solution manual of mathematic
CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose 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 Also, the use of differential equations in the mathematical modeling of real-world phenomena is outlined.Problems 1-12 are routine verifications by direc Solution manual of mathematict substitution of the suggested solutions into the given differential equations. We include here just some typical examples of such verifications.3IfSolution manual of mathematic
yt = cos2.V and y, = sin 2a-, then yi = -2sin2.V y2 = 2cos 2.V. soy* = -4 cos 2.V = -4yt and y2 = -4 sin 2.V = -4y,. Thus y '+ 4y, = 0 and y2 + 4y, = CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose of Section 1.1 IS simply to intro Solution manual of mathematic(', = (4e-") + 4(-2e-!‘)+4(c-!') = 0andy* + 4y:+4y, = (+ 4x Solution manual of mathematic 2a-. then y\ = - sin A- + 2 sin 2.V.yf = - cos A- + 4 cos 2.V. J>2 = cos A- + 2 sin 2a- . and y* = - sin A- + 4 cos 2.V. Henceyf+y, = (-cosa-+4cos2a-Solution manual of mathematic
) + (cosa--cos2x) = 3 cos 2a-andy* + y, = (-sin A-+ 4cos 2a )+ (sin A--cos 2a-) = 3 cos 2a-.1Copyright © 2015 Pearson Education. Inc2 DIFFERENTIAL EQUCHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose of Section 1.1 IS simply to intro Solution manual of mathematic~2 In X, then y' = x~' - 2 x‘- In X and y" = - 5 X-* + 6 x“ In X. $0 x2y" + 5xy + 4 y = x' (-5x"* + 6X-4 In X) + 5x(x'} -2x~? In x) + 4 (x"2 In X) = (-5x’:+5x’:) + (6x-2-10x’:+4x’:)lnx = 0.13Substitution of y = eF into 3/ = 2y gives the equation 3ren = Ze'. which simplifies to3r = 2. Thus r = 2/3.14 Solution manual of mathematicSubstitution of y = y* into 4 V* = y gives the equation 4r: eri = é*. which simplifies to 4r2 = 1. Thus r = ± 1 / 2 .15Substitution of y = en into y*Solution manual of mathematic
+ ý - 2y = 0 gives the equation r 2en + r - 20which simplifies to r +r -2 = (r + 2)(r-l) = 0. Thus r = -2 or r = l.16Substitution of y = e" into 3 y’ CHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose of Section 1.1 IS simply to intro Solution manual of mathematic3±V57)/6.The verifications of the suggested solutions in Problems 17-26 are similar to those in Problems 1-12. We illustrate the determination of the value of c only in some typical cases. However, we illustrate typical solution curves for each of these problems.17c = 218. c = 3Copyright © 2015 Pear Solution manual of mathematicson Education. IncCHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose of Section 1.1 IS simply to introCHAPTER 1FIRST-ORDER DIFFERENTIAL EQUATIONSSECTION 1.1DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELSThe main puipose of Section 1.1 IS simply to introGọi ngay
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