3. Give an example of a homogeneous function of the form f(r.y, 2) of degree 3.

Q: A necessary and sufficient condition that M(x,y)dx+N(x,y)dy=0 be a homogeneous equation is M and N…

A: A first order and first degree differential equation is of the form   M(x,y) dx + N(x,y) dy = 0  is…

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y),…

A: As per the policy, we are solving the first question. Please repost the question and specify which…

Q: 1. Find the first and second partial derivatives (that is f, af, , , and ) of Əx' dy' dx², ay² »…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: 4(a) Verify that the equation y = In x – In y is an implicit solution of the IVP, ydx = x(y + 1)dy…

A:

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: xfx+yfy=nf  f is a homogeneous of degree n

A:

Q: 10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and…

A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

Q: Determine y at t=0.2 (0.2) 0.8 by the fourth order Runge-Kutta method, given that y'=ity' y(0)=2

A: It is provided that y'=1t+y, y(0)=2. We need to determine y at t=0.2 0.2 0.8 by RK-4 method.

Q: Verify that the given functions are linearly independent by evaluating the Wronskian at x = = 0.…

A: Given a set of functions e2x ,  xe2x , cosx , sinx . To verify that the functions are linearly…

Q: Q2: Discuss the fundamental theorem for gradients using E = 5x2 i + 20 xy j+ 10 yz3 k and the…

A: Fundamental theorem of gradient states that a if  line integral through a  F gradient field depends…

Q: 11. Determine the solution of Utt = u (x,0) = 0, u (0, t) = h, where h, k, and A are constants. c²ur…

A:

Q: full solutions please, thank you

A:

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x,…

A: Topic:- calculus

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: We have to find degree of homogeneous function

Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: Which of the following is not a homogeneous function? h(x,y)= xª − 3xy³ + y¹ − x² cos Option 1 b(x,…

A: Let's solve.

Q: 1. The function y =0 is always a solution to a linear homogeneous OD 2. The ODE -(z+y+5) is…

A: 1. For linear homogenous OD equation whether there are trivial or non trivial solution x=0 is always…

Q: If f(x, y) is homogeneous of degree n and has continuous second-order partial derivatives, prove x…

A: Since f is homogeneous of degree n Let Since f is continuous second order partial derivative Hence…

Q: 4. Show that the Cobb-Douglas production functionQ = AK“L® is homogeneous of degree a + B and that…

A: Given Cobb-Douglas production function    Q=AKαLβ          A-constant First, we have to show  the…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Test the function def ined by f (x,y) = - x- 4y for its homogeneity. If it is homogeneous, give its…

A: Find your answer below

Q: Use the chcin rule to calcuuate the partial derivetives. 4v-2u g(x.y)= Sin (x?sy? ), X= u-V Express…

A: We have to calculate partial derivative by using chain rule. And we have to express derivative in…

Q: Let z(x, y) be the function implicitly defined as the solution to TC -2x + y + z + sin(xyz) = %3D…

A:

Q: i) Let f(x, y, z, p,q) be a homogeneous function of degree n of X, y and Z. Show that the equations…

A: (i) Given that f(x,y,z,p,q) is a homogenous function of degree n of x,y and z. Let We know that to…

Q: Given: f(x,y) = 2x²y³ and the points (1,2) and (1.1, 2.05) a.) Find f(1,2) and f(1.1,2.05). Then…

A: Here we want to find ∆Z using the function values and total differential.

Q: Find the value of the arbitrary constants in the given equation to satisfy the boundary condition: y…

A: The give equation with the boundary condition, yx=C1sinx+C2cosx; y0=1, y'π=1 use the derivative…

Q: - Find the solution u(x, t) of uz = conditions u(0, t) = 3 and u(1, t) = 2 and the initial condition…

A: Here, we are given the following system.       uxx=14ut, 0<x<1, t>0u(0, t)=3u(1, t)=2u(x,…

Q: Suppose that a, b, c, and d are constants such that ad- be # 0, and let m and n be arbitrary real…

A:

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

A:

Q: 1. Determine the types of the following partial differential equatio: (a) 4upa - 4uæy + Uyy 4uxy (b)…

A: According to the guidelines I am answering only first question.

Q: Which of the following is not a homogeneous function of x and y. cos () + sin a- cos y 2r - y 2+ 2xy

A: The function f(x,y) is said to be a homogeneous function of degree n if: f(x,y)=tnf(x,y)...(1)

Q: Form the partial cquatins by eliminating the fiam differential z- Qta) (?+b) atbiliary constant)

A: We have to form the partial differential equations by eliminating the arbitrary constants from…

Q: 10. Show that if f is homogeneous of degree n, then r* fn + 2ryfzy + y° fy = n(n – 1)f(x, y). (A…

A: Suppose that f is a homogeneous of degree n. To prove that x2fxx+2xyfxy+y2fyy=nn-1fx, y. By Euler's…

Q: a) a fonction f (xy) is homogeneous of degree 7 in X and y it and only it

A: As per bartleby guidelines we only give first question answers.

Q: 19. Let f(x, y, z) = + sin(3z) + e"-2". Find the rate at which f is changing at (2, 4,0) in the…

A:

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: (b) Show that the function f: R2 → R given by (* if (x, y) + 0, S(x, y) = 0 if (x, y) = (0, 0), is…

A:

Q: 1 3. Integrate the function f (x, y) = over the region bounded by x-axis, line x = 7, and the curve…

A:

Q: What is the degree of the following homogeneous function? * f(x, y) = On On-1 On-2 On-3 = xn +…

A:

Q: If the functions f(x², y²) and g(x, y) are homogeneous of degree 2 and 4, f (x, y) g(x, y) 1…

A:

Q: Find the partial derivative of z with respect to x дz (2x−y) дх Н дz 2 О 0 = 3 - 1 " дх Т 2y 2y дz…

A: Just use the rule of partial derivative and find the required solution.Final solution is in the box.

Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

A:

Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

A:

Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: Find a fourth order homogeneous linear ODE with solution x(t) = 3t² – 1+6e¯4. -4t

A: The given solution is xt=3t2-1+6e-4t. We have to find a fourth order homogeneous linear ODE with the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.