A solution of the heat equation for 0 < x < 2 is: 00 NT X u(x,t) = Cne-(na/2)²Kt sin n=1 Given that u(x,0) = x, for 0 < x < 2, show that cn = which you should find. A , where A is a constant n

Q: Let r(t) = 5 cos(t) and y(t) = 3 sin(t) All answers should be decimals rounded to 2 decimal places.…

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Q: O A snake is crawling on a surface. The temperature at a point (x, y) is given by T(x, y) = 70 + 5…

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Q: Ex/show that y = eax sinh bx satisfies y" - 2a y' + (a² + b²)y = 2 b2 e ax sinh bx

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Q: Find the general solution:

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Q: sin x – e-* = 0, [0,1]

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Q: using T= πT integration TT/2 dn= *2 O cos x cosnx dx

A: We know that: cosAcosB=cosA+B+cosA-B2∫cosaxdx=1asinax+C

Q: A snake is crawling on a surface. The temperature at a point (x, y) is given by T(x, y) = 70 + 5…

A: We need to use toral derivative to find change in temperature

Q: Find the rate of change of y with respect to x at the indicated value of x. sin(x) :- 11 - cos(x)' y…

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Q: Given sinh(r) = then tanh(r) = Select one: a. b. + C. + d. OS Shot by Hisense H12

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Q: Given: y' + y = y² (cosx - sinx) and y(0) = 2, Find C O A. 0 OB. 1/4 O C. 1/2 O D. 3/4 OE. None

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Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: Let F(æ) = | a cos(3t – 1) dt. sin a 1. Find F(0). 2. Find F'(x).

A: F(x)=∫sinxx2cos3t-1dtPut 3t-1=udifferentiate w.r.t t3dt=duput t=sinx then u=3sinx-1if t=x2 then…

Q: By using Beta function, the integral I tan(0) d0 is

A: To find value of integral∫0π2tanθ3dθ by using Beta function. Bm,n=ΓmΓnΓm+n…

Q: 6. Let sin x g(x) = [ Find g (7) 3 3 + -dt

A: Given; g(x)= integraion of sqrt[3/(1/4 +t2)], limit from 1 to sinx.

Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: العنوان > solve b cos (ln x ) d x (1-X²) X' 5/2 dx ۱/۱ S で T=T M

A: Here the integration formula has been use∫uvdx=u∫vdx−∫(dxd​u∫vdx)dx

Q: tan (x) + 1 dx =?

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Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

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Q: 5) consider the indefinite integral [cos ³ (x) dx. Explain why the Substitution U = COS (x) will not…

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Q: Ex/show that y = eax sinh bx satisfies y"- 2a y' + ( a² + b²)y = 2 b² e ax sinh bx

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Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: Solve using determining the integrating factor: cos x dx + (1 + 2/y) sin x dy = 0. %3D

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Q: x'=x.cot(t)+sin(t) a. find the general solution that satisfies x(1)=3

A: Let us consider a linear differential equation of first order of the form, dy/dx +P(x)y= Q(x) Then…

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.