Find the solution of the heat conduction problem 0 < x < 1, t > 0; 100uxx = Uti u(0, t) = 0, u(x, 0) = sin 3rx – sin 5x, t > 0; 0 < x < 1. u(1, t) = 0, sin 3äx u(x, t) =

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" +…

A:

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: tan²xdx = sin³ydy when x = 2, y = 3

A:

Q: Find f. f ''(t) = 3et + 6 sin t, f(0) = 0, f(?) = 0 f(t)=

A: Solution

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

A:

Q: y" - Y+1 = cos(+) u(

A:

Q: y" + y = sec x tan x

A:

Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

A:

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: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: x sin 4x2 dx

A: Integration is a process of finding the antiderivative of a function. There are basically two types…

Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

A:

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: y" + 4y' + 3y = sin (e*) %3D

A: follow next step

Q: y" +2y' = 3+ 4 sin(2t)

A:

Q: Find w, where w3 = 1 + i. i? = -1.

A:

Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

A:

Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

A: We will solve the problem

Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

A:

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: Question 6 Obtain the general solution to (D? + 1)y= secxcscx O y= C,cosx + C,sinx- cosxin|secx +…

A: First we put the auxiliary equation equal to 0 .then we find out the C.F. and then find out the…

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

A:

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: Which of the following is a solution to x' A(f) x +b (t) if -2 1 A (1) = -3 2 b(t)= 2 sin(t) -…

A: To find -

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: dy z = 3e*S, y = 3z2 + sin(z) S i5I dx %3D

A: Given,           z=3ex and y=3z2+sinz

Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

A:

Q: guess the form of the solutions 1- y’’ - 2y’ -3y = 3sin(5t)+tcos(5t)+2te^-t 2- y’’+2y+10y=4te^-t-…

A:

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Find y'' if y = 2x sin x. O O O A. y'' = 4 cos x - 2x sin x B. y'' = - 2x sin x OC. y'= - 4 cos x +…

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.