1.Find a general solution of each O.D.Es. A) y" 19y = coqx +os 3 - šin 2 (3) y" + 4y/ + 6.25у — 3.125(х +1)2. (2)y" 2x 3.125(x + 1)2.

Q: Could y = t^2 cos t be a solution of a homogeneous DE with constant real coefficients? If so, give…

A: The solution are next step

Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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Q: Use the method of undetermined coefficients to solve the initial value problem. Oy y = y= y = y = 3…

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Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 7x2 +…

A: Here we have to find ode of given solutions

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

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Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: 2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use…

A: Furst we rewrite the equation as in the theorem, then Use the given theorem

Q: The two parameter family of solutions of the DE: y" + 25y = 0 is y = c1 sin 5x + c2 cos 5x. Then,…

A:

Q: 5. Find two solutions (not multiples of each other) of the Bessel equation of order x*y" +xy' + (x²…

A: The general form of the Bessel equation is ,                                          x2y" +xy'…

Q: The solution to the initial value problem, y" + 4y' + 5y = cos cos 9x, y (0) = 0 is y (x) = ? ye(e,…

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Q: The IVP: y =t/y+ sin t; 1sts2, y(1)= 0, has a unique solution Select one: True False

A: Given, y'=ty+sint, y1=0, 1≤t≤2

Q: 1. Show that y(x) = c; sin 2x + c₂ cos 2x is a solution to y + 4y = 0.

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Q: 3. Find the general solution of y" – 3y + 2y = cos (e~-).

A: We use the method of variation of parameters to find the solution of y''-3y'+2y=cose-x First we find…

Q: (b) Find the general solution of d²q dq +60- +50q = 10 cos 2t dt dt² using the method of…

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Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

A: Solution

Q: 4. y" - 5y' + бу %3 -sin(2x)

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Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: If u(x, t) = D1 fn(t) sin(nx) is the solution Utt – 9ura = 2e2t sin(3x) + e-2t sin(4x) u(0, t) = 0 =…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Solve the initinal - value pYo blem dy COsx - Sinz +y 0Lx<0.5 y()=0 Using (a) four th- order Runge -…

A: Given differential equation                                                   dydx=cosx-sinx+y,…

Q: Give the general solution to xу +5ху%3D х 3 sin(4x). a) Oy = x cos(4x) + Cx-5 b) Oy = -* cos(4x) +…

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Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: 12. Verify by direct substitution that Un(x, y) = sin nx sinh ny is a solution of Uxx + Uyy 0 for…

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Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: When does an nth order, homogeneous, Cauchy-Euler equation anty(n) + an-1tn-ly(n-1) + +aity' + aoy =…

A: Given: nth order To find: Cauchy-Euler equation

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: 4. Solve the Cauchy problem Utt = 9uxx+cos x, (x, t) E Rx (0, ∞) u(x,0)=0, TER u(a,0)=0, x ER using…

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Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: Solve for the particular solution of the following non-homogeneous DE. y” – y’ = 2sin 2x

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Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

A:

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: 4.Find two solutions (not multiples of each other) of the Bessel equation of order 3232…

A:

Q: Find the solution of the given initial value problem in explicit form. 70 sin(2x) dx + cos(7y) dy =…

A: The given initial value problem in explicit form is sin2xdx+cos7ydy=0, yπ2=π7. Find the solution.…

Q: 2. Solve Un = Uxx X > 0, t> 0 with initial and boundary conditions given as u( x,0) = 1– exp(-x),…

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: Suppose that y1=e^x andy2=e^-x are two solutions of a homogeneous linear DE. Explain why y3=cosh x…

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Q: 9. Ify,(x)= sin 2r and y, (x) = cos 2x are two solutions of y"+ 4y 0, show that y, (x) and y, r) are…

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Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: Calculate Cos(y(2.500)) if y(x) is the solution of y" + 6y' + 9y = 13sin(2x) such that y(0) = y'(0)…

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Q: Find the solution of the given initial value problem in explicit form. 77 ㅠ sin(2x) dx + cos(8y) dy…

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Q: The solution of the nonhomogeneous DE y" + 4y' +4=5e* is

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Q: Find the general solution of the DE: dyldx = sin(7x) cos(5x) + cos(7x) sin(5x). O y = (-1/12)…

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Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: 2. Solve Un Uxx X> 0,t> 0 with initial and boundary conditions given as u(x,0) = 1- exp(-x), u(x,0)…

A: The D'Alembert's solution of one dimensional wave equation whose charactertics lines are ξ0=x-ct and…

Q: 4. y"+ 25y = 0; yi = cos 5x, y2 = sin 5x; y(0): y'(0) = -10 %3D %3D %3D 2x. u0)

A:

Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: The general solution of y"+ 16y3cost is: Select one: а. y = C, cos(4t) + C, sin(4t) + tcost 15 b. y…

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Q: Exer 1. Solve the following first-order boundary value problem 2 u +4 u, + 40 u = u(z, 0) = e* 60…

A: We have to find solution of given pde

Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

A: