4. Consider the DE: dy(x) = X - <- y(x), dx a. Sketch the slope field of the DE in fig. 3. b. Draw solutions through the points (-2,-3) (-2,-1) (-2,1) (-2,3). c. Conclusion: - in the slope field of this DE, all points on a line have the same slope. Figure 3

Q: (d) Let P = xy², Q = x²y and C denote one petal of the four leaved rose defined by r = -450<.…

A:

Q: 3. Given the slope field show to the right, answer the following questions. a. The associated DE…

A:

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given data:     The expression for the given electrical potential function is: V(x,y,z)=3x2-2xy+xyz.…

Q: is shown to the right. y The direction field for dx (a) Verify that the straight lines y = ±x are…

A: Hello, thanks for your question but according to our policy I am answering the first 3 subparts.…

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

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Q: Consider the slope field shown. (a) For the solution that satisfies y(0)-0, sketch the solution…

A: (a) The solution that satisfies the condition y(0) = 0 is sketched as follows: From the solution…

Q: dy 7. Which of the following could be the slope field for = x + y? (A) I|-1 |. (B) IIIIIII141111 -//…

A: given:- slope dy/dx = x+y

Q: An object is moving along a path defined by the graph  x^2+y^2=18 Compute  dy/dy, if dx/dt=-2,…

A: According to the question:

Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

A:

Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

A:

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A: Solution:-

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: (c) Use Laplace transform to solve y(t): y(1)-[,cly(x)dx =t.

A: As per instructions we are allowed to answer only one question. Laplace Transform: Let f(t) be a…

Q: 1²e¹dV where E is bounded by the parabolic cy E

A: the answer is give in step2

Q: Suppose that a particle following the given path c(t) flies off on a tangent at t = to. Compute the…

A: Consider the path of the particle           c(t) = (2t2, t3-4t, 0) The velocity of vector is…

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

A:

Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

A:

Q: Sketch the slope field for dy dt = t y for −2 ≤ t ≤ 2, −2 ≤ y ≤ 2.

A: Sketch the slope field:  dydt=ty for -2≤t≤2, -2≤y≤2. Construct the table of Values. t y dydt 0…

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A:

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

A: The given system is, where initial condition is x=0, y=0. Now taking Laplace transform of equation…

Q: compute CF d? for the veder field. KI+x3 xy> where Cis the line segment from CO.0) to Clo3)

A: The objective here is to calculate the integral: ∫CF→⋅dr→; Where F→=1+x2,xy2 And C is the line…

Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

A:

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

A:

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A: In this question, we have given a computer-generated direction field for the differential equation…

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin cz; x = y=t, z = t7 t'…

A: Here we have to find dw/dt by chain rule.

Q: Which of the following graphs is the slope field for 15/1 1~/1ST ~\~ in 13t-ii-i ~~~ -1 1 2 3 4 5…

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Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

A:

Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the parameter t 6. dt TO -/-

A:

Q: 1. Sketch the direction field and solution curve for the given DE and condition. Sketch the…

A:

Q: Sketch the slope field for dy/dt=y2-4. How do the solutions behave as t approaches infinity? Is end…

A: Given differential equation dy/dt=y2-4. Sketch of the given differential equation is shown below :

Q: Let F(t) = (e' cos t) î+ (e' sin t) ĵ + e' k. %3| (a) Find symmetric equations of the line tangent…

A:

Q: dy/dt = (y+1/2)(y+t) Use a slope field to explain why the solution that passes through (0,1) is…

A: A slope field is used to determine the approximate slope of the tangent at a point to the curve…

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

A:

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: dy 3. Draw the slope fields of = |t°lyat integer dt values on the grid and sketch the solution…

A:

Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

A:

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: 5. Consider the DE: dy(t) + ty(t) = 1, dt a. Sketch the slope field of the DE in fig. 4. b. Draw…

A: The slope field of given differential equation with solution curves is given as follows :

Q: 3. Given the graph of x' vs x, sketch the direction field for x(t) that corresponds. dx dt

A: Use the graph to draw the direction field. Observe how the graph passes through the visible points…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.