Show that, for any constants k' and 'a', u = sin(kx) sin(akt) is a solution of the equation Ut = a²ur.

Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

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Q: y" + 3y' + 2y = e¯ 2« – 10 sin(æ) - 10 -2x -

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Q: Find a particular solution to y" + 16y = -16 sin(4t). Yp ||

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: Find the exact solutions of vZ sin (x -)+ 1 = 0 for 0 sxs 47.

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Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

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Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: 3. [(3t +r*)sin (21)dt /

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Q: Find an antiderivative of the given function. 4 cos 9x O A. sin 9x O B. - 36sin 9x O C. sin 9x O D.…

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Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

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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: y = c, e2* cos 3x+C, e²* sin 3x

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: (sec(In x) y ху" + у' +:

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Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: Solve the D. E J+gtanx = sin ex

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Q: Prove that e* = cos x + i sin x by showing that each side is the unique solution to the initial…

A: Consider the differential equation

Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

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Q: (a) Use the method of undetermined coefficient to find the general solution to the inhomogeneous…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Find the general solution of y" – 4y' + 5y = sin (x)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: Show that where n is a positive integer.

A: To show

Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: find a linear homogenous constant coefficient equation with the given solution: y(x) =…

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Q: Find a particular solution to y" + 16y = -32 sin(4t). Yp !!

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Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: Find constants A and B such that yp(x) = A sin x + B cos x is a solution of dy/dx + y = 2 sin x.

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Q: Find the solution of the equation = e Cos y ax ay which tends to zero as x → 0o and has the value…

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Q: 2. Solve the DE: 2y' - y= 4 sin( 3x)

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Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

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

Q: y" + 25y = 10 sin(5t). Yp =

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Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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Q: Find the complete solution of the DE D´ (D– 1)y = 3e* +sin x.

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