Give the family of orthogonal trajectories of y? = Cx° + 5.

Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

Q: 3. y = C( Sec x+ tan x)

A: Note: we get orthogonal trajectories of families of curves by 1.differentiating  curve 2. Then…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: dy/dt-2ty=0

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = and the initial…

A: Givena(t) = <3,9t,et>

Q: f(0) is solve by using the following The orthogonal trajectories of the family of curves r=…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. y' =…

A: To solve the given differential equation by Runge kutta Method of order 4 first we fill find the…

Q: The time of oscillation, 1, of a pen- dulum is given by t 27 1. wherel is the length %3D of the…

A: Write this equation in standard form then diffrenciate.

Q: The position of a particle on the x-axis is given by (t) = t – 4t + 3. At what time is the…

A: solution:-position of particle is given byx(t)=t2-4t+3velocity, v(t)=ddtx(t)…

Q: (b) Find dE According to this model, if Cheryl is more tired than Desiree, but all other factors are…

A:

Q: The following equation describes the motion of a mass on a spring subject to damping, with a…

A:

Q: The position of a moving particle is given by s = t - 8t + 15, then its speed at t = 8 is

A:

Q: Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16,…

A: The differential equation of the damped motion is  my''+cy'+ky=0 with m=10, k=90 and c=10 That…

Q: The function u(x, y) = 2020xY is a solution of the Laplace's equation True False

A: The given equation is: ux,y=2020xy  The given function is a solution to Laplace's equation.

Q: If the position of a moving particle at any time 't' is defined by s(t) 3t-9t,0<t<6. The…

A:

Q: If z = xev, x = t and y = - 1+ 5t then: dz dt (Your answer should be in terms of the variable t.)

A:

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A:

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

A:

Q: The position of a particle moving along a coordinate axis is given by s(t)=t^3−9t^2+24t+4 for t≥0.…

A: For velociti differentiation of position vector And for acceleration derivative of velocity vector

Q: given the position function for an object in motion  is s(t)=-4t3+4t2-1 then the accelaration at t=1…

A: Differentiate the position function with respect to time t.

Q: Find the speed at time t = 2 seconds (s) of a particle whose positionvector isr(t) = t3i − etj + 4tk

A: Given position vector - r(t) = t3i-etj+4tkDifferentiating with respect to t to find the speed…

Q: sing the method of variation of parameters to e a nonhomogeneous DE with = -ex, W2 = e W2 = e-1Ix…

A: Wronskian of the function

Q: The position of a moving particle is given by s = 3t3 + 9, then its acceleration at t = 7 is O 27 O…

A: We will solve the following using derivative.

Q: /A: Given; y? = 6kx %3D Find orthogonal Trajector.

A:

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) =, and the initial…

A:

Q: Find ∫C (ez - 1) / z  dz with C being z(t) = eit for 0 ≤ t ≤ 2π

A:

Q: At time t 2 0, the velocity of a body moving along the s-axis is v=t2-7t+6. When is the body moving…

A:

Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A: Given that, An object with a mass of 10.00kg is launched from the ground with an initial upward…

Q: If the position of a moving particle at any time t' is defined by s(t) = t - 2t2 + 13. Then the…

A:

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A:

Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

A:

Q: The position of a moving particle is given by s 3t +9, then its acceleration at t = 7 is %3D 27 63…

A:

Q: 2. You are standing at the point (1,1,3) on the hill whose equation is given by z = 5y – x² – y?. !!…

A:

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

A:

Q: Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16,…

A:

Q: (a) What is the particle's position at t = 0? (b) What is the particle's position at t = 3? (c) What…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: The following equation describes the motion of a mass on a spring subject to damping, with a…

A:

Q: 5t3 dy Solve the IVP dt y(0) = -1. Show your work and explain thoroughly, when appropriate. y? +…

A:

Q: stimate the population will grow to P(t) (408)4, where t represents the number of %3D rding to this…

A:

Q: Maximise Z = 3 a + 2 b S.T. la - 1 b s 1 l a + lb 2 3 and both x and y are > 0

A:

Q: 4. Find the length of the curve Vē - 1 dt, y = 1<I< 16.

A:

Q: The expressions for and are dy A stationary point for z is

A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 16t - 12t, then the…

A: The position of a body s(t)=16t3-12t

Q: Q 6. Find the orthogonal trajectories of the functiony = x + ce, which is passing through (-2,0)

A:

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.