Find the solution of the heat conduction problem. 100uxx = ut,   0 < x < 1,   t > 0 u(0, t) = 0,   u(1, t) = 0,    t > 0 u(x, 0) = sin2πx - sin5πx,   0 ≤ x ≤ 1

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: Find the exact solutions of vZ sin (x -)+ 1 = 0 for 0 sxs 47.

A:

Q: = 1- Solve y"+6y' +9y=2xe * + 3 + 2x²

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

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A: Firstly find a homogenous solution and then find a particular integral . hence complete solution =…

Q: 3. y'=1+cosx−ycotx;y()= -ycot.x:y()= {y= /3 2 sin r 1 cot x+=sin x}

A:

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: + sin? x sec? xdx, 1.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

A:

Q: Integrate | 2 sin O de а. 3(cose)d

A: ∫2sinθ3(cosθ)2dθ

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Q: 2 sin(z) + V3 = o %3D

A: Given :   2sin(x) +√3 = 0               2sin(x) = -√3                  sin(x) = -√3/2…

Q: cot-1(t) Given F (x) = 1+sin=1(3x) 24 ot-1 . dt, evaluate F (0) and F '(0).

A: We have to find F(0) and F'(0).

Q: Question 2 Find the linear approximation of the function at the given point. f(x, v) = 3 sinx - 7…

A: F(x,y)=3 sin x - 7 cos y at ( 0 , π/2)

Q: sin x 4y" + 9y' – 7 = 4cos x

A: Solve by using rules of differential equations

Q: Find VV when (a) V = x² + y + ? y. (b) V = z sin (c)V = e+y+tz.

A:

Q: Find the solution of the equation zz + Əx² ay² ich tends to zero as x→∞ and has the value cos y when…

A: Given : ∂2z∂x2+∂2z∂y2=e-x cosy To Find : solution of the Equation

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

A:

Q: Find a particular solution to y" +4y = - 12 sin(2t).

A:

Q: a" + 4x = sin t %3D Solve the initial value problem | ¤(0) = 1, æ' (0) = 2 a) x(t) = sin 2t + cos 2t…

A: Given: x'' + 4x =sin t      ...(1)  with initial conitions:   x(0) =1,…

Q: eginning with the homogeneous version of ODE, find the characteristic e = ext. olve the…

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Q: Solve nxx = ut in Rx (0, 0) with u (x, 0) = 5 cos (6x) + 7 sin (10x)

A: Given partial differential equation is uxx​=ut​ with the condition u(x,0)=5cos(6x)+7sin(10x). To…

Q: Let r(t) = Find 7¹ (t) r¹' (t) = < " V

A:

Q: Verify that y = c sec² x is a general solution of y' = 2y tan x, where c is an arbitrary constant…

A: We varify that given solution is solution of given differential equation by differentiating the…

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

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A:

Q: A particular solution of y" + y = sinx + xcosx

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.