Find the dy + 9 Cos Cx)= 3 Cos Cx) paihular suluhon Of the differenhal epeccin sahisfying the mihal Cunch hon g Co) = S

Q: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: FIND THE GIVEN DIFFERENTI Homogeneous Eguation ( 3x + 4y) dx - dy -0

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Q: Give the number of oscillations occurring per second for a spring-mass system that obeys the simple…

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Q: Solve the following DEQ by separable method: dy (cos x + 1)( sin y – 1) dx

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Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

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Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: az and dz Use the chain rule to find as at sin(0) r = st, 0 = s9 + t° %3D as az at

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Q: the area outside r = 1 and inside r = 2 cos 0 is

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Q: S cos“C)dy

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Q: and casy=0t, and DLyr, Furd the exact alue of tan Ca-y.

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Q: Which of the following is a left Riemann sum approximation of (x²) dx with n subintervals of equal…

A: Definition used-                  Left-hand Riemann sum -                   ∫abf(x)dx=…

Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: d - [sin(t) dt = 0, Where k is cons tan t dx Select one: True False x

A: Here, the integral has the constant limits 0 and k. So, ∫0ksin(t)dt s in terms of k that is…

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

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Q: Fird the Aren of the Reyion c2-9 cos In teriur of (2€)

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Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that Wi is a standard Brownian motion and consider times 0 < s <t<o∞. Find E[W,W¿] and hence…

A: Given: Wt is a standard Brownian motion  0&lt;s&lt;t&lt;infinity

Q: Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation Lz of a function fz at the point z=z0 Lz=fz0+f'z0z-z0

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

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Q: au Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson approximation to…

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

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Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

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Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: L[t cos 2t

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Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: Use an appropriate local linear approximation to estimate the value of co Gos(29°) &

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Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

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Q: Al/ compute 6(4+ ec©*) dx + (siny + 3x?)dy cosx Where c is closed bounded region lying in the first…

A: Given (A) The given integral is ∮4+ecosxdx+siny+3x2dy and the region lies in between x2+y2=4 and…

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: does not exist. (b) If u = x cos y+ye", where x=s+2r and y = st , prove that ди ди dt = (s – 21) (x²…

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Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu

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.