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Math Advanced Math ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

(a) To graph: The portions of the direction field of the ordinary differential equation. The differential equation is written as: y ' = y + x d y d x = y + x The direction field of ordinary differential at the interval − 5 ≤ x ≤ 2 , − 1 ≤ y ≤ 5 shown in From the figure 1, it can be observed that the direction field is parabolic shape at the interval − 5 ≤ x ≤ 2 , − 1 ≤ y ≤ 5 . (b) An ODE with the general solution and draws the direction field. Differentiate the given implicit equation with respect to x. d ( x 2 + 9 y 2 ) d x = d ( c ) d x 2 x + 18 y d y d x = 0 d y d x = − 2 x 18 y d y d x = − x 9 y The direction field of ordinary differential is shown in figure 2. From the figure 2, it can be observed that the direction field is semi ellipse and similar work for circle, Hyperbolas, Parabolas and other curves. (c) To draws: The direction field of the ordinary differential equation d y d x = − x y . The ordinary differential equation is written as: d y d x = − x y y d y = − x d x Integrate the above differential equation. ∫ y d y = − ∫ x d x y 2 2 = − x 2 2 + c 2 2 y 2 = − x 2 + c 2 Where c is the arbitrary constant. The direction field of ordinary differential is shown in figure 2. From the figure 3, it can be observed that the direction field is circle. (d) To draws: The direction field of the ordinary differential equation d y d x = − y 2 . The ordinary differential equation is written as: d y d x = − y 2 2 d y y = − d x Integrate the above differential equation. 2 ∫ d y y = − ∫ d x 2 ln y = − x + ln c 2 ln y − ln c = − x On further simplification, the following is obtained. ln y 2 2 = − x y 2 2 = e − x y 2 = 2 e − x Where c is the arbitrary constant. The direction field of ordinary differential is shown in figure 3. From the figure 4, it can be observed that the direction field is parabolic shape.

(a) To graph: The portions of the direction field of the ordinary differential equation. The differential equation is written as: y ' = y + x d y d x = y + x The direction field of ordinary differential at the interval − 5 ≤ x ≤ 2 , − 1 ≤ y ≤ 5 shown in From the figure 1, it can be observed that the direction field is parabolic shape at the interval − 5 ≤ x ≤ 2 , − 1 ≤ y ≤ 5 . (b) An ODE with the general solution and draws the direction field. Differentiate the given implicit equation with respect to x. d ( x 2 + 9 y 2 ) d x = d ( c ) d x 2 x + 18 y d y d x = 0 d y d x = − 2 x 18 y d y d x = − x 9 y The direction field of ordinary differential is shown in figure 2. From the figure 2, it can be observed that the direction field is semi ellipse and similar work for circle, Hyperbolas, Parabolas and other curves. (c) To draws: The direction field of the ordinary differential equation d y d x = − x y . The ordinary differential equation is written as: d y d x = − x y y d y = − x d x Integrate the above differential equation. ∫ y d y = − ∫ x d x y 2 2 = − x 2 2 + c 2 2 y 2 = − x 2 + c 2 Where c is the arbitrary constant. The direction field of ordinary differential is shown in figure 2. From the figure 3, it can be observed that the direction field is circle. (d) To draws: The direction field of the ordinary differential equation d y d x = − y 2 . The ordinary differential equation is written as: d y d x = − y 2 2 d y y = − d x Integrate the above differential equation. 2 ∫ d y y = − ∫ d x 2 ln y = − x + ln c 2 ln y − ln c = − x On further simplification, the following is obtained. ln y 2 2 = − x y 2 2 = e − x y 2 = 2 e − x Where c is the arbitrary constant. The direction field of ordinary differential is shown in figure 3. From the figure 4, it can be observed that the direction field is parabolic shape.

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

10th Edition

ISBN: 9781119809210

Author: Kreyszig

Publisher: WILEY

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Chapter 1 Solutions

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - 9–15 VERIFICATION. INITIAL VALUE PROBLEM...Ch. 1.1 - Prob. 16P Ch. 1.1 - Half-life. The half-life measures exponential...Ch. 1.1 - Half-life. Radium has a half-life of about 3.6...Ch. 1.1 - Prob. 19P Ch. 1.1 - Exponential decay. Subsonic flight. The efficiency...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES Graph a...Ch. 1.2 - 1–8 DIRECTION FIELDS, SOLUTION CURVES Graph a...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES Graph a...Ch. 1.2 - Prob. 4P Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES Graph a...Ch. 1.2 - Prob. 6P Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES Graph a...Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - Autonomous ODE. This means an ODE not showing x...Ch. 1.2 - Model the motion of a body B on a straight line...Ch. 1.2 - Prob. 13P Ch. 1.2 - Prob. 14P Ch. 1.2 - Prob. 15P Ch. 1.2 - Prob. 16P Ch. 1.2 - EULER’S METHOD This is the simplest method to...Ch. 1.2 - EULER’S METHOD This is the simplest method to...Ch. 1.2 - EULER’S METHOD This is the simplest method to...Ch. 1.2 - EULER’S METHOD This is the simplest method to...Ch. 1.3 - Prob. 1P Ch. 1.3 - Prob. 2P Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION Find a general solution. Show the...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs) Solve the IVP. Show...Ch. 1.3 - Prob. 20P Ch. 1.3 - Radiocarbon dating. What should be the content...Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Prob. 29P Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - Prob. 36P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - ODEs. INTEGRATING FACTORS Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS Test for exactness. If...Ch. 1.4 - Exactness. Under what conditions for the constants...Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.5 - CAUTION! Show that e−ln x = 1/x (not −x) and...Ch. 1.5 - Prob. 2P Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS 7. xy′ =...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS 9. Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS Find the...Ch. 1.5 - Prob. 14P Ch. 1.5 - Prob. 15P Ch. 1.5 - Prob. 16P Ch. 1.5 - Prob. 17P Ch. 1.5 - Prob. 18P Ch. 1.5 - Prob. 19P Ch. 1.5 - GENERAL PROPERTIES OF LINEAR ODEs These properties...Ch. 1.5 - Prob. 21P Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs Using a method of this section or...Ch. 1.5 - Prob. 29P Ch. 1.5 - MODELING. FURTHER APPLICATIONS 31. Newton’s law of...Ch. 1.5 - Prob. 32P Ch. 1.5 - MODELING. FURTHER APPLICATIONS 33. Drug injection....Ch. 1.5 - MODELING. FURTHER APPLICATIONS 34. Epidemics. A...Ch. 1.5 - MODELING. FURTHER APPLICATIONS 35. Lake Erie. Lake...Ch. 1.5 - MODELING. FURTHER APPLICATIONS 36. Harvesting...Ch. 1.5 - Prob. 37P Ch. 1.5 - Prob. 38P Ch. 1.5 - Prob. 39P Ch. 1.5 - Prob. 40P Ch. 1.6 - Represent the given family of curves in the form...Ch. 1.6 - Prob. 2P Ch. 1.6 - Represent the given family of curves in the form...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs) Sketch or graph some...Ch. 1.6 - APPLICATIONS, EXTENSIONS 11. Electric field. Let...Ch. 1.6 - Electric field. The lines of electric force of two...Ch. 1.6 - Prob. 13P Ch. 1.6 - Conic sections. Find the conditions under which...Ch. 1.6 - Prob. 15P Ch. 1.6 - Prob. 16P Ch. 1.7 - Prob. 1P Ch. 1.7 - Existence? Does the initial value problem (x −...Ch. 1.7 - Vertical strip. If the assumptions of Theorems 1...Ch. 1.7 - Change of initial condition. What happens in Prob....Ch. 1.7 - Prob. 5P Ch. 1.7 - Maximum α. What is the largest possible α in...Ch. 1.7 - Prob. 8P Ch. 1.7 - Common points. Can two solution curves of the same...Ch. 1.7 - Three possible cases. Find all initial conditions...Ch. 1 - Prob. 1RQ Ch. 1 - Prob. 2RQ Ch. 1 - Does every first-order ODE have a solution? A...Ch. 1 - What is a direction field? A numeric method for...Ch. 1 - What is an exact ODE? Is f(x) dx + g(y) dy = 0...Ch. 1 - Prob. 6RQ Ch. 1 - What other solution methods did we consider in...Ch. 1 - Can an ODE sometimes be solved by several methods?...Ch. 1 - Prob. 9RQ Ch. 1 - Prob. 10RQ Ch. 1 - Prob. 11RQ Ch. 1 - Prob. 12RQ Ch. 1 - Prob. 13RQ Ch. 1 - Prob. 14RQ Ch. 1 - Prob. 15RQ Ch. 1 - DIRECTION FIELD: NUMERIC SOLUTION Graph a...Ch. 1 - Prob. 17RQ Ch. 1 - Prob. 18RQ Ch. 1 - Prob. 19RQ Ch. 1 - Prob. 20RQ Ch. 1 - Prob. 21RQ Ch. 1 - Prob. 22RQ Ch. 1 - Prob. 23RQ Ch. 1 - Prob. 24RQ Ch. 1 - Prob. 25RQ Ch. 1 - Prob. 26RQ Ch. 1 - Prob. 27RQ Ch. 1 - Prob. 28RQ Ch. 1 - Half-life. If in a reactor, uranium loses 10% of...Ch. 1 - Prob. 30RQ

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