We noted tnat Newton's Law of Cooling/ Heating can be modaled by te IVP, AT - hlT-Te), T6) = TE dt - Stabe Newten's Law and define all variableo and constants. - Solue the IVP uoing an integrating facor. - Suppose you preheat your ouen 325° and you want to bake from the refrigerator (32) inte the ouan. If it takio 1.25 hours for the temperature of your bind to reach 170° what io tu heat loss oefficient? to you plae alouely chicken

Q: Evaluate A. 2/3 B. 4/3 */2 12 000 C. 1/3 D. 5/3 [zdz r²dr sinu du.

A:

Q: EX-3- A particle moves along a straight line so that after t (seconds) , its distance from O a fixed…

A: BY THE RULES SINCE YOU HAVE NOT MENTIONED WHICH PART. I CAN DO ONLY FIRST THREE PARTS.   Velocity is…

Q: Use function f Gx)= X-cos(x) to %3D differedtinte Newton's fined Poird method and methed.

A: Given that f(x)=x-cosx The newton method is, xn+1=xn-f(xn)f'(xn) Then f'(xn)=1+sin x So, the…

Q: Solve the ODE of variable coefficients first changing this to constant coefficients x²y" – 4xy' + 6y…

A:

Q: d 17. t?e" dt dx

A: We have to solve

Q: 35. tet sin 5t dt

A: Given:∫0∞te-t sin5t dtUsing general formula of Laplace transform:∫0∞e-st ft dt = fs=LftLsinat=as2+a2

Q: y = sin³ 2x جد مشتقة الدالة

A: To find the derivative of y=sin3 2x, we have to use the chain rule. Chain rule:…

Q: de cos² 0

A:

Q: Solve Variation of parameters to find y. and Yp and y y" + y = secxtanx

A:

Q: solve et (l-t)? with y coJ=2 and y'Co)=6

A: We have to solve

Q: sinx find f"(0). 4. If A) = %3D C. a. e d.

A: Please refer to the image below

Q: vor use two and three Points 1 Gaussian Guadrature 2 (1+sinx) dx = I

A: Given integration is I=∫02πe1+sinxdx Let f(x)=e1+sinx Formula for two point method is…

Q: 12y-y=e

A:

Q: Part IV. Solve the given problem. Show your solution. The electronic force for an electric circuit…

A:

Q: @ yーJ=ex 12 y3=

A:

Q: S sin Vat dt

A: Let the given integral be: I=∫sinat dt

Q: 12 y"-y=e

A: Please refer the attached image for complete solution.

Q: 10 · S (sech u + tanh u)² du

A:

Q: Find [COR cosh’(t) sinh(t) dt . 2

A: To find the following integral.

Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: Seax sinh ax dx ах

A: Given integral is  ∫eax·sinhax dx To evaluate the value of given integration, we will use the…

Q: y= log, sinx

A:

Q: sinh (u + v)= sinh u. cosh v+ cosh u. sinh v и.

A: Consider the Identities for hyperbolic functions and expand the given expression.…

Q: Am + bm = S2m = ame™™ + bme¯ L V' 2| dy sin シ (v-) =[V +(-1)"(v' – v)]. тлу L am

A: Here m≠0.

Q: If the solution to the equation y"+ by'+cy 0, is y(t) = Ce cos(t) + cze sin(t), then, the values of…

A:

Q: If sinh(æ) = -4 , then coth(x) = (A) (B) =VI7 (C) =VE V15 (D) 4 15 (E) E O (A) O (B) o (c) O (D) O…

A: Solution

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.