6.14 Determinc the solution of the Dirichlet problem for parabolic equa- ди , а и дх2 а и дхд әt u(x, -1) = u(x, 1) = x2, u(-1,t) = u(1,t) = 1². - 2xt- +2² а и at2 - Г ди дх tr - u = 0,

Q: Q2: Solve the following differential equation in two ways. (2xy+x²)dx + (x² + y² )dy = 0

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Q: Q18) The formula of the particular solution yp of y) + 4y"=3 sin(2t) - 5cos2t, is: a) y₂ = Asin(t) +…

A: The particular solution to be assumed for the functions to solve the differential equation using…

Q: Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are): a) 0,1 b) 0,-1 c) 0 d)-1 021) - (1)…

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Q: 9. Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y"…

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Q: Q24) The general solution for y' = by x, is: a) = 3x² + c b) ² = x² + c c) == 3x² + c d) == x² + c y…

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Q: Q20) The singular point (s) of (x + 1) y' + x²y = 0, is (are): a) 0,1 d)-1 b) 0,-1 c) 0

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Q: Verify the orthogonality condition of each of the equations y" - 2xy' - 2ny = 0 11 ( where n is a…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: +2y" -y'-2y = 0, is: Q10) The general solution of y" a) y(x) = c₂e²x + ₂x + c₂e* c) y(x) = c₂e²x +…

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Q: +8+20 +8+20 Q14) If the power series method was used to solve the following ODE. 1 (x-0.5)y" x+0.5…

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Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: (1 3./ x' -5 : %D 2m1

A: The eigen value for the matrix 1-52-1 using calculator are -3i and 3i with eigen vector 1-3i2 and…

Q: Find the general solution to y" +(-1) y' + (- 12) y = 5 e2'. %3D a. None b. 7.e2 t y=c, e3t+c, e4t+…

A: To find  The general solution of the given differential equation.

Q: b) ta 1 -atsinst Q23) 1 = a) (5-3)2+25/ 5 024) The general solution for y' = 6y²x, is: b) est sin3t…

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Q: [Acos(5x) + Bsin(5x)] Q16) Combine the following power series expressions into a single power…

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Q: Q15) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant…

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Q: Solve y/ 3D (1 + y) sec (х) + tan (х) Оа.z- (у+ с) [sec (2) — tan (z) оь. т3 (с - у) [sec (х) + tan…

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Q: a) y₂ = Asin(t) + Bcos(t) c) y₂ = Asin(2t) + Bcos(2t) b) yp= Atsin(t) + Btc Ур d)y= Atsin(2t) + Be 1…

A: To find- ∫0∞e-st dt Here , we will use the integration formula- ∫eaxdx=eaxa

Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

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Q: a) s² L(y(x)) + sy(0)-y'(0) c) s² L(y(x))-sy(0)-y'(0) Q12) The kernel of the Laplace transform Q13)…

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Q: Find the solution to the given homogeneous linear ODE. (4D5-23D³-33D²-17D-3)y=0 - 3x y=e¯³ (C₁+C₁₂x)…

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Q: Г3 4 -27 Q2. a) Suppose A=|2 1 1 2 – 4 and b(t) =| 0 then find the solutions of the given dX system…

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Q: d) (2n+1)(x-2)" Q17) If you know that the radius of convergent of the series method for the ODE…

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Q: Ge + c₂0 c) y(x) = c₂e²x + c₂e² Q11) L(y") = a) s² L(y(x)) + sy(0) - y'(0) c) s² L(y(x))-sy(0)-y'(0)…

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Q: 12 2 5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ] Euler - Lagrange equations for…

A: To find the Euler-Lagrange equations for the given Lagrangian L, we need to calculate the partial…

Q: Q1:- A) solve the following D.E '5 x?y" + 1 - B):- у" + у' — бу %3D 8е3х

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Find the solution of BVP ۱۰uny U₂+2; u(0,4)=0 2 ux (2,0) = X₂

A: As per the question we are given the following boundary value problem (BVP) : uxy = ux + 2  ;…

Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: - (y-2u) + u, y = -2 x- y, u(x, 1) = e. find an explicit solution for u = u(x, y) sub

A: Introduction: A partial differential equation is known as Lagrange's type if it is of the form…

Q: c) s² L(y(x)) -sy(0)-y'(0) Q12) The kernel of the Laplace transform of f(t),t> 0, is: d) s²…

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Q: Use the method of Variation of Parameters to solve y" -y' = t.

A: The given differential equation y'''-y'=t. We have to the differential equation using the method of…

Q: Verify that the vector X is a solution of the given homogeneous system. 1 -1 x-( )xx-(7)** X'= 4 X;…

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Q: Consider the system of differential equations Y1 + 3y2, %3D 3y1 + Y2, %3D with solutions Y1(t) Y2(t)…

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Q: 5. Find the general solution of (x + y + 1) dx + (x – 3y - 7) dy = 0 %3D x? - 3y? + 2xy + 2x x? +…

A: To find the general solution of the given differential equation