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

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: Y"+y=secxtanx by using annihilatior methode

A:

Q: Find the singularity of the function f(z)=(e^z-1)/z at z=0.

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Q: Find the L^-1 iNVERSE LAPLACE d.)F(S) =3/4s

A: Inverse Laplace transform of (1/s) is 1 .

Q: Determine the yy''' + 2x = tanx dependent variable independent variable type pde/ode order degree…

A: The given differential equation is yy'''+2x=tanx We have to determine dependent variable,…

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 6. A particle is travelling along the circular path x² + y² = 100. At the moment when the particle…

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Q: Let z =e^2x Tany find ((d^2 z)/(dxdy)) and ((d^2 z)/(dydx))

A: Given z = e2xtany

Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

A:

Q: Consider y = xe^x on the interval [-5, 0]

A: In order to find global minima of the function, check the values of the function at end points and…

Q: Find 1. y = ar' + br constant) + cr+d (a, b. c.d

A: Given ,  y = ax3 + bx2 + cx + d      (a , b , c , d constant) We have to find dy/dx We know that ,…

Q: x^1/4 + y^1/4 = 2, What is y'' at (1,1)?

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

A:

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: Find xp by implicit differentiation. S 4e*"y = 2x

A: According to the given information, it is required to find the implicit differentiation.

Q: 3. Differentiate x²+1 () ± ([** 1 dt 4 1+ sin“ t d dx

A:

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

A:

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: In the derivative, transform into linear equation y = mx + b (the form)

A: Given :  y = mx + b (the form)   To find : In the derivative, transform into linear equation

Q: S*(1+v*) -\dv (cot-ly2) 2.

A:

Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

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Q: Find dt dt dy dx dt dt "I and 1층 x = stet y = 2t + sin(t)

A:

Q: (a) [10pts| y' = (x2 – 4)(3y + 2), y >0 dy 3y+2 = dx (x-4) » yt=ce >y=ce -en lyt > en cyt=) =…

A: Follow 2nd step.

Q: y"+2+y=e^5t y(0)=0 У (0)-5

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Q: Apply appre printe method to work ant the optimal oution f given moblem. Maximige GNo.5 z = 3x+22 +3…

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Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: Зх- 1 | (*-9) dt Use Leibniz's rule to find for y = dx

A: Leibniz's Rule:ddx∫a(x)b(x)f(x,t)dt = f(x,b(x))·db(x)dx +  f(x,a(x))·da(x)dx - ∫a(x)b(x)∂f(x,t)∂xdt…

Q: Solve following Couchy probiem . the 2x e^uxy -Uxx +Ux =ye uloy) -0, Ux(0,y) =승 y %3D

A:

Q: prove that | Sinsy | dy лу ∞

A:

Q: please give step by step answer.   let X have the PDF fx(x)={X^3/4,0<x<2 0,elsewhere a)let Y=X^2…

A: The problem can be solved using the concept of pdf. please find step by step solution below.

Q: Draw a direction field for the equation y'=y+x-y^2 for -5 < x, y

A: The direction field is obtained as follows:

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.