s) find the general sduton of second dilferential equation 3y"+2y'+y=0

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: Solve the follo wing in itial Value problem by using laplace trans formi- 9y =0 ; yl0) =0 and…

A:

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: SupposeThat w=XYz+XY +Z+3andx=3cost, %3D Y=35int, z=27, Evaluete dwl dtt= I 2

A: solution.

Q: Match the D.E. with a direction field: y' = t+ y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2…

A: NOTE: The horizontal axis is t-axis.

Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: dy/dt-2ty=0

A:

Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

A:

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

A:

Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P…

A:

Q: Use the vectorized Euler method with h = 0.5 to find an approximation for the solution to the given…

A: Given the differential equation      y''+3ty'+y=0 with y(0)=4, y'(0)=0 on [0,2]. Step size, h=0.5…

Q: (t + z cos(t)) dt + (sin(t) – 3z² + 5) dz = 0

A: Let's find.

Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

A:

Q: d?z dz +3- 2z = te-2t dt z(0) = 0 ; z'(0) = -2 dt2

A: Given differential equation is, 2 z'' + 3z' - 2z = te-2t z(0) = 0; z'(0) = -2

Q: Find an equation of the tangent plane at P = (0, 3, – 1) to the sur- face with equation ze* + ez+1 =…

A:

Q: The velocity field for a fluid is given by V=(X2t3)i+(2XYT)j. The convective acceleration in the…

A: Given, V=x2t3i^+2xytj^ Here, u=x2t3 and v=2xyt Convective acceleration in y-direction is given by:…

Q: Let Y1, Y2,..., Yn N(µ, 4), where is the unknown parameter. Find the MVUE for µ².

A: Fisher-Neyman factorization theorem: Suppose X1, X2, …, Xn is a random sample of size n taken from a…

Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: 3. Find the orthogonal trajectory of y = c sin x.

A:

Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

A: The position vector of the particle is given by  r(t) = 2t2, t3, -1

Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx²…

A: Let us consider the wave equation ∂2u∂t2=∂2u∂x2, 0≤x≤1, t≥0 and L=∆x=0.25; K=∆t=0.1 Consider x=ih…

Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: Sketch the direction field of the D.E. y = y - t and the solution curves corresponding to y(0) =-1,…

A: Solution of question is written in below steps.

Q: If y(u) = Cos v -dv then y'(u) =

A:

Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: Use the vectorized Euler method with h=0.5 to find an approximation for the solution to the given…

A:

Q: dz Find given: dt z = zew, z = t°, y = - 5+5t dz Preview dt II

A: This problem can be solved as follows:

Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P…

A:

Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)

A:

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

A:

Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

A:

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: dz/dt = -Bz(1 – vz), z(0) = 1. %3D

A:

Q: Use the vectorized Euler method with h=0.5 to find an approximation for the solution to the given…

A:

Q: d.x = -2x + 5Y dt dy -2.x + 4y dt 5 cost X = \ sin t et 3 cost –

A:

Q: Q1) Find equation of plane normal to vector 3i + 2j – k and pass through point (1,1,5).

A:

Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: 2,d'y(0) = -2 dt? d'y(t) , dy(t) dy0) - + 3 dt = sec(t), y(0) = 2, dt %3D %3D dt

A: Answer

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

A:

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

A:

Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

A:

Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

A: