B شعبة a5f 1- Show that O for the following equation in less than three steps only f (x, y) = x2 + 5xy + sin x + 7e* 2- Find aw when u = - 2 if w W = XV + In(z) r = V =11+ V 7= 0C OS u V=

Q: Q.5 Solve the BVP V²u = uzz + Uyy = 2, Uz (0, y) = uy(47, y) = 0, u(x, 0) = 0, U(x, 7) = 2 sin () 0…

A: Given equation is  ∇2u=2 , 0<x<4π , 0<y<πux0,y=uy4π,y=0uxx,0=uyx,π=2sinx4 Now, let the…

Q: The equations xy? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 3u²v² = 9 are solved for u and v as…

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Q: State Leibnitz's theorem. If V1- x² y =sinx, then prove that (1-x) yn+2– (2n+1) xyn+1=n°yn= 0.

A: The Leibnitz theorem is used to generalize the product rule of differentiation. It states that if…

Q: f'uo) -22:2294 W = 0.4748 2nd Stetzation flui) = fla4748) = 31e flui)= 0.0044 f'ni)= flouT48) = -31e…

A:

Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

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

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x, y) and v(x, y) in f(2) where f(z) is…

A: We will find out the required values.

Q: 7. F(t) = [sin (t -) - cos (t -)u (t -) | 8. F(t) = 8 sin cos t 9. F(t) = cos cos (; – bt) - bt), b…

A:

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 3(2 + cos t)3 +c Use the appropriate substitution to evaluate the following integrals: . sint (2+…

A: Solution is given as below:

Q: The equations re + uz – cos(v) - 2 = 0 and u cos(y) + 10x2v – 10yz2 – 1 = 0 can be solved for (u,v)…

A:

Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Substitute c4 = -c3y in the equation (6), Y() = 0 (7) Substitute the value of X (x) from equation…

A: To give explanation to the solutions of the equations X''-a2X=0 & Y''+a2Y=0.

Q: Use an appropriate substitution to integrate 2. A sin u +c 12r'sin (x?– 2) +c © 12sin (x2- 2) +c…

A: To evaluate the given integral.

Q: Let t> 0, 1 > x> 0 x = 0 or x = T, t>0, t = 0. 1, 4:(x,t) {0, %3D sin x, 0 sxST, (a) Show that u, is…

A: Given Boundary Value Problem ( A )  : ( ∂2∂x2-∂∂t )u =0  , 0< x< π , t> 0…

Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

A: Given,

Q: uesuon o of 8 Determine the general solution (du/dt)3-(du/ dt) "2-2u = Select the correct response…

A:

Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

A: use partial differentiation for finding the derivative.

Q: 1 3s 11. Set F(s) = +e s/2 +s s2 +1 {, 0 7/2 1+ cos r, (a) 1+3 sin x - cos r, 0 n/2 1- cos x, (b)…

A:

Q: (4e + 10z-3 sin r)dr =. O 4ez + x10-3 cos T + c O 4e + x +3 sin a + c O 4e* + x10-3 sin r + c | O…

A:

Q: Use the method of separation of variables to solve :=0 in (0,1) × (0,+0), (2) u(0,t) =u(1,t) =0,t…

A:

Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

A:

Q: 4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx…

A:

Q: Q1: Solve the IBVP ut + u = V'u u (r, y, 0) = 0, u (x, y, 0) = cos z sin 3y %3D Uz (0, y, t) = u (T,…

A:

Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: 9. z = xe-; P(1,0, 1) 10. z = In /x² + y²; P(-1,0, 0) 11. z = e³y sin 3x; P(7/6,0, 1) 12. z = x/2 +…

A:

Q: 1) x² + y² + ² = 3, P. (1,1,1) 2) 2=-x²=0, P. (2,0,2) XZ 3) cos(x)=x²y + e + yz = 4, P. (0,1,2)

A:

Q: 3. Using integration by parts (IBP), what should you pick for u and du in 5z cos(3r) dr? = cos(3r),…

A: Integration By Parts formula is used for integrating the product of two functions. This method is…

Q: 4) Solve via separation of variables: u(0, y) =0 ди -(2, y) = 3sin a'u a'u +5 sin =0 ; 6. S0<x<2…

A:

Q: 17. (D4 + 2Dz + 1)y = 5 – 3x² a. y = (C1 + C2x) cos x + (C3 + C4) sin x – 3x² + 17 b.y = (C, + Czx)…

A:

Q: (9. Solve u, +u,, = 0_for0<x<1,0<y<1, given u(x,0) = 0, u (x,1) = 0, u(0,3) = 0, u(l,y) =1. 9. u(x,…

A:

Q: A) u-substitution with u = 7x³ +5 B) u-substitution with u = 3x² u-substitution with u = 3x² dx…

A: Integration

Q: Q.3 Use ODE methods to solve the BVP: U = 18xy + sin(2x- y) U(0, y) = y -cos y, U(x,0) = x² -cos2x,…

A:

Q: Find constants C, such that u(x,y) = 2 C, sinh nx sinny is the solution of the problem: %3D ou du =…

A: Image is attached with detailed solution.

Q: 8. The auxiliary roots of the auxiliary equation associated with a certain homogeneous LDE are m =…

A: Solution of question as follows

Q: (D³ – D²)y = cos2t; y a. y = C, + C,t+ Cze +cos2t-sin2t 10 20 b. y = C, + Czt + Cze-2* cos2t + 10 1…

A: We have to find the general solution of the given  differential equation D3-D2y=cos2t .

Q: (). %3D e2(s-6)²+25)) u (t – 2) (cos 5t + sin 51) O u(t – 2)et cos(5t – 10) ,6t | - u (t – 2) er-12…

A: We will find out the required value.

Q: 8. The auxiliary roots of the auxiliary equation associated with a certain homogeneous LDE are m =…

A:

Q: I. Fill the table in. CN Z1 Z2 No. Rec Pol Exp 1. 5- j5 2. 152-34° 3. Z3 25ein 4. Z4 -13-j12 5. Zs…

A: Since you have asked multiple questions, we will solve the Q.8 and Q.9 for you. If you want any…

Q: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the value dt of t given.

A: NOTE : As per Bartleby guidelines, incase of multiple questions only one will be answered. Please…

Q: 7. (D + 4D² + 4D)y = cos x 4 a. y = C, + Cze-2* + Czxe¬2* . 25 cos x+ 75 sin x 4 b.y = C, + Cze¬2* +…

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Q: The general solution of xy" – 2xy' +3y = 0 for x +0 is y = %3D 이미이2e1 cos( In |z|) + c2 sin(1In…

A:

Q: 47. y"+3y' + 2y = 4e* 49. y"-4y' + 4y = 2e2x 51. y" + 4y 53. y" + 9y = 2 sec 3x 55. y"+4y 57. You…

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Q: 1) Find ôz l ôu and ôz lôv for z= 4e* In(y), x= In(u cos(v)), y=u sin(v) at the point (u, v)= (2,7 /…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: sin If y = , then justify (1–x² )n. -(2n +1)xy, – n² y,-1 =0 applying Leibnitz's a) theorem.

A: Please check step 2 for the solution.

Q: Solve the equation Ax b by using the LU factorization given for A. %3D 3 0 15 0 0 0 0 1 3 1 1 2 0 10…

A: Here,

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.