Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х + Be+ Cx cos(4 x) +Dx sin(4x) +E -4x b) O z=Axe + Be+ C cos(4 x) +D sin(4 x) c) z=Axe*+ Be + Cx cos(4 x) +Dx sin (4 x) + E -4 x d) O z=Axe + Be+ Cx cos(4 x) +Dx sin (4x) +E e) z=Axe*+ Be + C'cos(4 x) +D sin(4 x) + E f O None of the above.

Q: 3, Find the poner sertes solution in poners of (x-1) of *最+y=o; 0 2 +2y=0j つ4 4(メー)-4(メー)れ +…

A: Given that xy''+y'+2y=0 Take y=c0+c1(x-1)+c2(x-1)2+c3(x-1)3+c4(x-1)4+c5(x-1)5+.. Take the derivative…

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: 6. Find the general solution of the system: :) X+(- sint X = -2 cos t

A:

Q: What is the particular solution of the function 2²e%z sin 3x? O (Aæ² + Ba + C) cos 3z + (Ea² + Fx +…

A: NOTE: Refresh your page if you can't see any equations. . now consider only   for that, the…

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

A:

Q: Under what conditions on A and B does the B.V.P x'y" - 3xy' +3y = cos x, solution, no solution ,…

A: Given equation is, x2y''-3xy'+3y=cosx Take the homogeneous term, x2y''-3xy'+3y=0 Take y=xn,…

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

A:

Q: Let 47x + 20 y = 2 is a linear Diophantine equation 1) Show that 47 x + 20 y = 2 has integral…

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: This is the solution of the Cauchy - Euler equation xy" + 5xy' + 20y = 0 %3D O y = C1x4 cos(4 ln(x))…

A:

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

A:

Q: Give the general solution to у" — 4 у'+ 20 у 30 а) О у-С, сos(4 х) — С, sin(4 x) b) O y=C, e**+C, e…

A:

Q: What is the complete solution of -2+y = +y=x-2-2 cosx. a.) y. = Ae*+ Bxe* + sin x - cos x b.) y, =…

A:

Q: Let 38 x + 16 y = 2 is a linear Diophantine equation 1) Show that 38 x + 16 y = 2 has integral…

A: A linear Diophantine equation ax+by=c  has integral solution if GCD(a, b) / c Solution is x=x1-nbGCD…

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

A:

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

A: Solution

Q: Given that y, = 5 cos t is a solution to y"-y'+y = 3 sin t, and y2= 5 e2t is a solution to y" -y'+y…

A:

Q: What is the general solution of (D® + 20Dª + 100D2) y = 0 Oy = C + C2x + (C3 + Csa) cos 10r + (C4 +…

A:

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

A:

Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

A:

Q: what is the general solution of y''+4y=cos(2x)

A: Given: y''+4y=cos(2x)

Q: 14. A form of a particular solution for the DE (using undetermined coefficient method) + 3yl4 + 5v"…

A:

Q: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

Q: Show that 6r- t= In 2r- is an implicit solution of the DE : dz (6r-1)(1-2r). dt Give the explicit…

A:

Q: 2. Differentiate y os=1(-2x³ – 3)³ = cOs

A: From the given problem:   y=cos-1-2x3-33   As we know that:   cos-1x=-11-x2   So,…

Q: The second-order difference equation Yk+2 - 3yk+1 + 2yk = 2 sin(3k) (4.164) has the homogeneous…

A:

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

A:

Q: Use the method of undetermined coefficients to solve the initial value problem. O y y = y = y = 33…

A:

Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: 9. Use the method of undetermined coefficients to solve the given system sin t X' X + %3D -2 cos

A:

Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

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

A:

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

A:

Q: y" - 5y'=x-2, when x = 0, y = 0, y = 2

A:

Q: How do you solve this problem?

A: Note: As the question is very lengthy, we have showed the important calculations leaving the basics.…

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

A:

Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

A:

Q: Let 38 x + 16 y = 2 is a linear Diophantine equation 1) Show that 38 x + 16 y = 2 has integral…

A: Using the result: if gcd( greatest common divisor) of two integers 'a' and 'b' is 'c' then there…

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: What is the general solution of (Dº + 16Dª + 64D²) y = 0 %3D O y = C1 + (C2 + C4r) cos 2/2x + (C3 +…

A:

Q: find the particular solution to the general solution y(x) = c1x +c2+ x^2 -1 if y(1) = 1, y’ (1) = 2…

A:

Q: Find the general solution of y +9y-4 cos 2r A. y -A cos 3x +B sin 3x +c cos 2r B. y -A cos2xr + B…

A: Given: y''+9y=4cos2x

Q: Solve x4) +6x³y/3) + 25x²y +19xy` +81y=0 where x>0 O c, cos(3/nx) + c,sin(3/nx) + C3cos(3/nx)inx+…

A:

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

A:

Q: 4 Give the general solution to x²y' + xy = -2 cos(2x) y¯2

A: The solution is given as

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

A:

Q: Example 1.4: Is y(x)= c, sin 2x + C2 cos 2.x, where trary constants, a solution of y" +4y = 0? and…

A:

Q: What is y' if y=x³sin (x²)? a. y'=2r°cos (x²) + 3x²sin (x²) b. y'=2r*cos (x²) + 3x³sin (x²) c.…

A: Solve for the derivative

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

A: