3) Solve the following heat equations: part a) Find the solution u(t,x) to 2εu = 4uxx t>o, Oo u(0,x)=2x-1 06x-1 part 5) Find the solution u(t,x) to ·2tu = 44xx t70, Ocxcl ux (+, 0) = ux (+1)=0 t>o 4(0,x) = x² 06X61

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A: The solution is given as

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

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A: To find out the characteristic equation.

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A: Given that the heat equation ∂u∂t-∂2u∂t2=0withu(0,t)=u(1,t)=0with ICu(x,0)=u0(x)

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Q: Зу" — бу' + 6у%3D е' sec x

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

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A: Given that the nonhomogeneous system                      X'=AX+g, where                A=21-5-2,…

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A: The given opinions and incorrect. There can't be x in power. In particularly x(-x/2) can't be…

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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 =…

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Q: X42 then

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

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A: As per the instruction, we will be answering the part (b). For (b), We are given the following…

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A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A: To find the values of constants, we need to plug the given function into the differential equation.

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A: To find the values of constants, we need to plug the given function into the differential equation.

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Q: (d) Find all possible values of a, b, c so that U(x, t) = ax² + bt + ct² solves the heat equation…

A: To find the values of constants, we need to plug the given function into the differential equation.

Q: لام ( = = 3 e + 2 = 1 * " - 49 + 2 +49 - ax له +2 ه = 4 + 4 + 4 - 2 4 = (0) و ر ۱ = (0) × 1 = (Xo…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…