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: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: у" — у' — х*е* + 5 + сos x

A:

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: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

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

A:

Q: Writing Systems in Matrix Form. In each of Problems 1 through 8, state whether the given system is…

A: Solution:-

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: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

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

A:

Q: Solve vxx + vyу %3D ху ,х € (0, п), у € (0, п ) v(0, y) = 0 v(п, у) %3 sin2y vх, 0) — sin3x v(x, 7)…

A: Given: vxx+vyy=xy   …1, x∈0,π, y∈0,πv0,y=0vπ,y=sin2yvx,0=sin3xvx,π=0 We have to solve equation (1).…

Q: Perform the summation below using the following set of data: 4, 5, 5, 6, 7, 8. Σ (422 - 5)

A: The answer for the given summation problem is 830

Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

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: f"(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 4 f(0) = -sin (0) - cos(0) + (0) + 2 x

A: Given the ordinary differential equation:.The aim is to find the function f.Integration Formula:

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: Find the largest interval on which the LV.P (x +(4) x -5) y" + sin(x) y' + y =0, y(0)= 3, y'(0)=4…

A:

Q: what is the privet Solution to the equation (0'+0)y(x)=Xsinc) (X)

A: Given: The differential equation is D3+Dyx=xsin x. To find: Particular solution to the equation.…

Q: Given that y = C, tan x + C, sec x is a family of solutions of the equation y" –(tan x)y' -(sec? x)y…

A: Here given differential equation y''-(tanx)y'-(sec2x)y=0 Family of solution of the differential…

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an…

A: SUM OF A SERIES :-  The sum of a series is the limit of its n-th partial sum sequence.

Q: y" + y = sec (x)

A:

Q: Solve F'(t) = t+ F(t – u) cos u du, F(0)-= 4. %3D

A:

Q: x²e*= sin(x² yz) Let f(x, y, z) %3D 12 o f find dydzd' x at the point (2, 0, 0)

A: Expanding the terms as power series then differentiating

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

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.