What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

Q: let w=ln(x2+y), x= 2t, y=4-t. compute dw/dt a) using the Chain rule, draw corresponding tree diagram…

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Q: What does Cauchy's EU Theorem 6.2 guarantee for the IVP dy/dt = -(y^2)/2t , IC: (t_o,0) a solution…

A: The given equation is  dydt=-y22t I.C. =t0,0

Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Let A = Av = ( 4(Av) = ( -3 4 3 21.₁ ‚ v = (x, y).

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Q: Please solve the following PDE: Af(t, x,y) af(t,x,y) _ {\f(t,a,y) = a2, f(0,x, y) = za² zz2 + + x-…

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Q: J(u) = [ (x2 + u(t)²)dt min s.t. dri = 12 dt dr2 dt T1(0) = r2(0) = 0 x1(1) = 1 and r2(1)…

A: As per the question we have to find the optimal control law u* , which minimizes J(u) And we will…

Q: OPnd w if ww=fcカっ) find メ= Sint dt

A: We have to find d2wdt2, Where w=f(x,y) and x=sint , y=t2 We will get  d2wdt2 by differentiating w…

Q: H.W:- Used Cramer's Rule to find the value of the variables in the following equations: 5x + 4y = 11…

A: Creamers rule is used

Q: Evaluate S(ti + tj + t°k)dt = i+ j+ k.

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Q: If F (x)= [V5t² – 3t dt find F'(3). a) 0 b) Viz c) d) 3 e)

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Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: f(2) 1 dt, then f'(z) = ++1

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Q: In the context of ordinary least square (OLS): Given mịn- ||Y – Xß||? Use derivatives to derive the…

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Q: a) b) d'y(t) _2d'y(1) dªy(1) _4dy(t) + 5y(t) = 6x(1) dt' di' dt¹ dt d'y(1) di' dit Property +2dy(t)…

A: Linear: A differential equation is linear if the unknown function and its derivatives are to the…

Q: is A+Ce^(-kt) a general or particular solution to the DE dT/dt=k(A-T)

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Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: Find Laplace treins form for Ý +4Y+3Y = e y(o) =y co) = 1 %3D %3D

A: Formula Used:L{y''}=s2Y(s)-sy(0)-y'(0)L{y'}=sY(s)-y(0)L{eat}=1s-aL{tneat}=n!(s-a)n+1

Q: Evaluate s's' √y³ +1 dy dx

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Q: Find o r(t)dt if r(t) = (cos t, sin t, 3t²). %3D O A.O B. (0, 2, ³) OC (0,0, x³) O D. (0, 2, 7) O E.…

A: We have to choose the correct answer from the given option

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: dx x²-6x+18

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: d ef dt (F(=") = %3D dz dz 13

A: We have to find

Q: [y = = V +2 u?-1] 3 Vx2 + 2 u2+1.

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Q: (p;-q,)? 2. Prove that KLD(p||q) = J6 t Eisisn pitt(ai-p) dt. %3D

A: Given: To show the given statement as follows: KLD (p|| q) = ∫01t ∑1 ≤i ≤ n pi-qi2pi+i( qi- pi) dt

Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…

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.