Let us consider the following problem for the heat equation ôu d’u = 0 in (0,1) ×(0,+∞), ди -(0,t) ди “ (1,t) = 0,t > 0, (1) u(x,0) = sin x,0< x<1. Use the method of separation of variables to solve problem (1).

Q: Convert the following 2nd order IVP to a 1st order system IVP, by viewing y' as a second dependent…

A: Given: We have to convert the given 2nd order IVP to a 1st order system IVP, by viewing  as a second…

Q: 3. y" +2y' + y = 2 sin t H(t – n), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost+ (t+1-)e™-']H(t–n) %3D

A: The given differential equation is: y''+2y'+y=2 sin(t) H(t-π) ;              y(0)=1,   y'(0)=0

Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

Q: H. JJ HY BY 4.6 where y(0)=0 y'co)=2

A: Given differential equation is y''+4y'+3y=4e-x with y(0)=0 and y'(0)=2We know the formula that PI of…

Q: Particular Solution   cot x (y' + 1 ) 2y = 0, y (π/4) = 9

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Q: Use variation of parameters to find a particular solution, given the solutions y 1, 2 of the…

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Q: I Solve the differential eauations 4. (D7D+19D+13)y =0 when x-0, y=0, y'=2, y"= -12, find y()

A: Given differential equation is D3+7D2+19D+13y=0 and given when x=0, y=0, y'=2, y''=−12 that is y0=0,…

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

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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: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: I need the answer as soon as possible

A: As we know that, eiz=cosz+isinz                   ...(1)And,e-iz=cosz-isinz                ....(2)…

Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

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Q: find the interval of the inicial value

A: Given Data: Let us consider the given data, t-6y'+t-2y=lnt+t-1 , y3=-4. To find the interval of…

Q: (a) y=In, X-4 2x+5

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Use method of successive approximation to solve the Deifferential equations up to 3 substitutions…

A: , We have to solve differential equation using successive approximation method.

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: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: y" +2y+3y= sint + 8(t-3л); y(0) = 0, y'(0) = 0

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Q: y" + y = sec (x)

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Q: 9. Which of the following equations are separable? Write those that are separable in the form y' =…

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Q: dy Find for y= csc (x)+ dx cos (x'+1). Do not simplify your answer. dy dx Given the equation x' + y'…

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Q: 1. You are going to build a giant Ferris wheel near Limketkai Mall. Given two endpoints of a…

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Q: Suppose that, p* is a market equilibrium price such that Qª = Q* = Q*. So the system of equations of…

A: Consider the provided question, We have to find the derivative dQ*dθ and dp*dθ. Since , at…

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.