Find the value df (a) that Make ECX) is Contincity at X- Ž

Q: y"-uy'+5y= e Sin() %3D

A: We have to solve given problem:

Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: dy 2х + ху is separable. dx y2 + 1

A:

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

A:

Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: 2 c2 Reverse order and evaluate the integral S, 2y2 sin(xy) dydx

A:

Q: Ev aluate the double integral dy dx 3/x

A:

Q: Q,7 Evaluate the integral 1) L,x* dx 2) xVx+1 dx 3) f cos2xdx

A: we have to solve

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: Q3) Approximate the integral e* cos x dx using the composite Trapezoidal rule with M=5 subintervals.

A:

Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: Solve the Ro liowing B E 2 X + 2 -zey= zX

A:

Q: Find the general solution: dy = tanxtanydx %3D

A:

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

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

A: Given function is, fx=100sin6πx at x=0 and x=L Now, we know that, ∂2t∂x2+qgk=1α·∂t∂z....(1)

Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

A:

Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

A:

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: 5 一=A+hxsl-x dy=?

A:

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

A:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

A:

Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

Q: Solve the initial-value pxoblem dy dr COSX-Sinx t %3D yro)%3D0 Using Adams. Moulton.

A: Given differential equation is dydx=cosx-sinx+y Let  f(x,y)=cosx-sinx+y                 (1) 0≤x≤0.5,…

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

A:

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: dx-(it 2x tany) dy-0

A:

Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

A:

Q: tion of the separable equation dy 23 3 +2)³ + 2)?

A:

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: E valvate cox³ (x²+3)dx 2.

A:

Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

A:

Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

A:

Q: Q5:- Find the integral dx n=8 using Trapezoidal method.

A: Given that: ∫15exxdx   n=8  using Trapezoidal method.

Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

A:

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

A: