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

Q: Ax, y) = sin(xy), r(t) = (e²t, e³), t = 0 %3D

A: Solving by differentiation we have

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

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

A:

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

A:

Q: consider che funceion h= w²-8.Tawei Determine dh/dt and w= St"-26

A:

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

A:

Q: Solve the following Cauchy problem on half-line: Utt = Uxx u (0, t) = 0, u(x, 0) = x, ut(x, 0) =…

A:

Q: 11 FCF)dt= fCx) dx =- 43 then 1.

A:

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

A:

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…

Q: Let f(x) = (2a² – 8) (5æ + 8) 13 %3D f'(x)

A: Given:         fx=2x2-865x2+813         differentiating on both sides      f'x=ddx2x2-865x2+813…

Q: Find the solution of the wave equation when initial velocity equal to O and initial deflection is…

A:

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.