q17 S + 7(A) Y(S) =s4 (s2 + S - 1)s4 + S3 + 3B Y(s):s3 (s2 + S - 1)$5 + S4 + 6© r(s) =s4 (s2 + S - 1)6.DY(s).s4 (s2 + S - 1)s2 + 3E Y(s).s3 (s2 + S - 1)S3 + S + 1(FFY(s) =(s2 + S - 1) Given the differential equation and its initial conditionsy" + y' - y = t3 with y(0) = 1 and y'(0) = 0Use the Laplace Transform rules for derivatives to convert this function into F(S) and then solve for Y(s).L{ y(1)} = Y(s)L{ y'(1)} = S Y(s) - y (0)L{ y"(t)} = s2 Y(s) - Sy (0) y'(0)

Introduction: A higher-order linear differential equation with initial conditions can be solved by…

Answered: S + 7 A Y(s) s4 (s2 + S 1) s4 + S3 + 3…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2
Find the slopes given by the differential equation y'= y-2 at each of the following points: a. (0,0) b. (1,1) c. (-2,4) d. (4,-2) e. (-3,-3) f. (5,12)
Match the differential equation with its direction field. y' = sin(10x) sin(10y) 20) -0.31 1-0.2 \ +0x1 \ \ 0- - 0.2 / /03 -0.3- 0.2 -0.1 0.1 0.2 -0.3 -2 -1 1 -2 -1 1 0.3- Give reasons for your answer. The slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 0, and y' > 0 for 0 < x < n/10, 0 < y < n/10. O The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 10. o y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x. | |||
1. Find the derivative of (a) (b): X-4 2x+5 y=In|csc x– cot x) (a) (b) (c) Find the differential dy: y=csc² x y=In, 2. A ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is S= 80t-16ť² (a) What is the maximum height reached by the ball? (b) What is the velocity of the ball when it is 96 ft above the ground on its way up? On its way down? 3. Find an equation of the tangent line to In x X at the point (1,0). the curve y= 4. The legs of an isosceles right triangle increase in length at a rate of 2 m/s. Determine each. X X Z (a) At what rate is the area of the triangle changing when the legs are 2 m long? (b) At what rate is the area of the triangle changing when the hypotenuse is 1 m long? (c) At what rate is the length of the hypotenuse changing?
Newton’s theory of gravitation states that the weight of a person x feet above sea level is given by:
1
Solutions to the differential equation = xy also satisfy = y'(1+ 3x?y²). Let y = S(x) be a particular solution to the differential equation dx 3 xy with f(1) 2. (a) Write an equation for the line tangent to the graph of y = f(x) at x = 1. (b) Use the tangent line equation from part (a) to approximate f(1.1). Given that f(x) > 0 for 1 < x <1.1, is the approximation for f(1.1) greater than or less than f(1.1)? Explain your reasoning.
What is the differential equation of all parabolas with axis parallel to the y-axis? Select one: O y" = 0 O y'" + yy" = 0 O 2xy" – yy' = 0 - o y'y" – 3y"2 = 0 //2
Find the differential of each function. (a) 2 + 5s 2 dy = (3s + 2)2 (b) y = e" cos(u) 1 dy = e "(sin(u) + cos(u))
Form the differential equation of family of lines situated at a constant distance p from the origin.
y'=x/((1+x2)2)cos2y solve differential

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S + 7 A Y(s) s4 (s2 + S 1) s4 + S3 + 3 B Y(s)= s3 (s2 + S - 1) s$ + s4 + 6 © r(s) s4 (s2 + S - 1) 6. O Y(s) : s4 (s? + S - 1) s2 + 3 E Y(s) s3 (s2 + $ – 1)