Let u = 36(1+2x), v =y-2, f=z+ + and df be the differential (linear) approximation of f(2.2,4.9,1.1)-f(2,5,1). Then V 10df =

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A:

Q: A. Expand, that is, perform the indicated operations on the differential operator D. 1. xD(D + x) 2.…

A:

Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

A:

Q: Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: ) Solve by using Laplace transform the partial differential equation 0² a² y dt² =9. ox² y(0,t) = 0,…

A: Solution

Q: Let p and a be continuous functions, and let y and yo be solutions of the differential equation /+…

A: Solution; Consider the given differential equation: y'' + p(t) y' + q(t) y = 0 We have given that y1…

Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

A:

Q: 11. Show that U(x, y, z) = (x² + y² +z²) satisfies Laplace's partial differential equation + = 0.

A:

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: Integrate the following three differentials over the three paths from (3/2,0) to (7/2,1) as shown in…

A: we have  dF=5x2+2xydx+6y2dy for path 1 x=32⇒dx=0and y=1 we get dF=6y2dy∫ABdF=∫016y2dy⇒FB-FA=2y301…

Q: find Ly for the given differential operator if (a) y(x) = 2e3x, (b) y(x) = 3lnx, (c) y(x) = 2e3x…

A:

Q: SOLVE THE PARTIAL DIFFERENTIAL EQUATION BY LAPLACETRANSFORM uz(x, t) + u¿(x,t) = sint given that…

A:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: Let z = f(x,y)= x^3+ xy+ y^4    (a)  Use differentials to estimate Δz as x changes from 1 to 1.05…

A:

Q: Find the differential equation defined by the transfer function : 2+2s+1 g3+252+4s+2 O d'e + 2 + 4…

A: We will find out the required differential equation.

Q: The order and degree of the partial differential equation respectively 26 z 7 dz () + x = y? is, dy…

A:

Q: Let u = 36(1+3x), v =y-2, f=z+, and df be the differential (linear) approximation of f(2.2,4.9,1.1)–…

A:

Q: For the differential equation: dy/dx = 2x + y, compute dy/dx for x = -2, -1,0,1,2, y = -1,0,1 and…

A:

Q: Solve by using Laplace transform the partial differential equation 0² = 9. y(0,t) = 0, y(2,t) = 0,…

A:

Q: Use the method of reduction of order to find a second independent solution of the given differential…

A: Use reduction of order method

Q: Let u(x,y) = X(x)Y(y) be a solution of the following partial differential equation (PDE): du du = (x…

A: To solve the below partial differential equation. ∂u∂x−∂u∂y=x+2u

Q: 1-t2 is 1+t2 The differential of u= In,

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the solution of the Differential equation by using Laplace Transformation: 1) 2y' – 3y = e2t…

A: 1) Given equation is  2y'-3y=e2t, y0=1 Taking Laplace transform , we get…

Q: By assuming that u(x, y,t) has the product form u(x, y, t) = 4(x+ Vt)ø(x – Vt)Y9y), separate the…

A:

Q: Find the differential equation defined by the transfer function : s+1 2s2+s+2 + 2c = + 2r +c = + 2r…

A:

Q: Let u = 36(1+5x), v =y-2, f=z+, and df be the differential (linear) approximation of f(2.2,4.9,1.1)-…

A: Linear Approximation:

Q: Classify the given partial differential equation as hyperbolic, parabolic or elliptic a?u a²u du + 2…

A:

Q: Ql: verify that the indicated pair of functions is a solution of the given system of differential…

A: Given equations are x=e-2t+3e6t and y=-e-2t+5e6t. Compute the derivative with respect to t.…

Q: at f(x,y,z) = z exp(− x2 + y2 4z ) satisfies the differential equation ∂2f + ∂2f = ∂f ∂x

A: To prove that                 ∂2f∂x2+∂2f∂y2=∂f∂z Where,         f(x, y, z)=1ze-x2+y24z

Q: Consider the partial differential equation du at' du (0, t) = 0 and u(37, t) = 0 for t > 0. with…

A: Given heat equation is ut = uxx

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? А)…

A: Find orthogonal trajectory

Q: 1-t2 is 1+ t2 The differential of u=In, 2t dt tA – 1 A du= B du=| dt =(_2t dt t4 – 1 D) none of the…

A:

Q: Let p(x) = be the standard integrating factor to y' + p(x) y = q(x). If y, 11 x2+14 x+ 13 is one of…

A:

Q: Assume that p, q : S' → R are continuous and p + 0. Find all solutions of the differential equation…

A: Given: Let us consider the given p,q:S1→R are continuous and ∫S1P≠0 and determine the al solutions…

Q: Find the particular integrals of the following partial differential equation to represent surfaces…

A:

Q: The differential operator (D2 - 16D+113)³ annihilates the functions

A:

Q: Verify that the function u(x,y,z)=1/√(x2+y2+z2)  Is a solution of the following differential…

A:

Q: verify that the given functions are solutions of the differential equation, and determine their…

A:

Q: 4. (a) Verify u(x, t) = e-,rE R',t> 0 satisfies the following partial differential equation: %3D…

A: A scalar function f(x,t) is a rule that is used to associate a number or quantity with a particular…

Q: Let (2x In (y) + u(x)) dx + v() ) dy = 0, + v(y where u(x) and V(y) are differentiable for all X and…

A:

Q: ) Solve by using Laplace transform the partial differential equation a² y d'y =9 y(0,t)= 0, y(2,1)=…

A: Solution:-

Q: Find u from the differential equation and initial condition. du - e1.9t – 3.7u u(0) = 3.2. dt

A:

Q: SOLVE THE PARTIAL DIFFERENTIAL EQUATION BY LAPLACETRANSFORM u(x,0) = 0 u(0, t) = 0 u,(x, t) +…

A:

Q: x"(t) + 9x(t) 5sin (2t) when t = 0,x = 3,x' = 1

A: Solve the differential equation by using Laplace transferom

Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: Show that u(x, y) = x"f(t), t = y/x, satisfies the differential equations ?u ди + дх ду (a) x- хо…

A: Given differential equations: (a)  x∂u∂x+y∂u∂y=nu (b)  x2∂2u∂x2+2xy∂2u∂x∂y+y2∂2u∂y2=nn-1u First we…

Q: Find the transfer function G(s) = C(s)/R(s), defined by differential equation + 3c = 3 + 5r. Assume…

A:

Q: 23. Let z = f(x, y) = 2x* – y. [6.2] a) Use differentials to estimate Az when x = 3, y = 2, Ax =…

A: Given that z=fx,y=2x4-y2, x=3,y=2,∆x=0.01, and ∆y=0.02