16) Find the solution to the nonhomogeneous heat equation: Uxx = t( sin 2πx + 2x), 0 ≤x≤1, t> 0 PDE: ut BC: u(0, t) = 1, u(1,t) = t² IC: u(x, 0) = 1 + sin 3x - x

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: find the general solution for  2 Z_xy+ Z_yy =cos( y) +1

A: Firstly find a homogenous solution and then find a particular integral . hence complete solution =…

Q: The solution of 1y"+ y' = 0, y (0) = 0, /(0) =1 /(0) = 1 %3D is y(a) = %3D (A) cos a (B) sin a (C)…

A: The solution of a differential equation must satisfy the differential equation. Check the options…

Q: Find the general solution of dy + y cot(x) = 6 csc'(x). dx

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Q: Ut = Uxx e-3t sin(5x) + e−²t sin x, -2t u(0,t) = u(T,t) =0, u(x,0) = sin(2x).

A: Introduction: Laplace transformation and inverse Laplace transformation is very significant in…

Q: x· y'+xy=0 (>0): y(0) = 0, y'(0) = 0, y" (0) = (g) ey"+sin x y" + cos x I .

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Q: Find the general solution:

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Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

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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: Solve b part only now in 10 min

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Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: Зу" — бу' + 6у%3D е' sec x

A: Given differential equation, 3y''-6y'+6y=exsecxy''-2y'+2y=13exsecx

Q: y" +2y' = 3+ 4 sin(2t)

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Q: Solve the IVP: y" +9y= u(t-1) y(0) = 1, y'(0) = 2 Solve the IVP: Solve the IVP: y" - 4y' + 3y =…

A: Note :- '' As per guidelines we will solve the first question. If you want any specific question to…

Q: y" + 4y" +y' – 6y = 2e¬t + 5 cos t y" + 4y' = 16 sin 2t , y(0) = 2, y'(0) = -2, y"(0) = 4

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Q: |u₁₁ + εu₁ = c²uxx tt |u(0,t)=0, u(L,t)=0 u(x,0)=sin(x), u₁(x,0)=0 Use separation of variables to…

A: As per the question we are given an IBVP in terms of the damped wave equation (with damping term ε).…

Q: Use the annihilator operator (not undetermined coefficient) for the right hand side and use it with…

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Q: a" + 4x = sin t %3D Solve the initial value problem | ¤(0) = 1, æ' (0) = 2 a) x(t) = sin 2t + cos 2t…

A: Given: x'' + 4x =sin t      ...(1)  with initial conitions:   x(0) =1,…

Q: s to find a particular sy1, y2 of the s(x))y'+(sin(x) - cos(x)) y = e 2 = e-* cos(x)

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²y"+xy'+(x² – })y =…

A: Hint: particular solution of a differential equation from method of variation of parameters suppose…

Q: Solve nxx = ut in Rx (0, 0) with u (x, 0) = 5 cos (6x) + 7 sin (10x)

A: Given partial differential equation is uxx​=ut​ with the condition u(x,0)=5cos(6x)+7sin(10x). To…

Q: Determine a suitable form for a particular solution for the DE: y(5) + 2y(4) + 2y" + 2y" + y' = 3t +…

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Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

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Q: Use the d'Alembert solution to solve 1 0u 9 dx2' u(x, 0) = cos? x, u(x,0) = e"+1. -0 0, t > 0,

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Q: x - ; )* ( sin 2t X' |X + 4 2 \2 cos 2t)

A: We have to solve the system of equations.

Q: Find the particular solution : y" + y' + 4y = cos3x 3 5 3 5 (a) cos3x -; sin3x (b) Yp = cos3x -…

A: Proceed as shown below...

Q: Find the general solution of y" + 12ly = 0. Oy(t)=c₁e-12¹+c₂e Oy(t)=c₁e¹¹+c₂e Oy(t) = c cos 11t+c…

A: This question is about ordinary differential equation.

Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

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