The solution of the initial boundary value problem * U, = 4u, u (х,0) - 0, u, ( x,0) = x(1– x), u(0,t) = 0, 0 < x<1, t> 0, 0

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A: Given, Bwalya was born in 1980. We know that 1980 is a leap year. Also, we have a leap year come…

Q: Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear…

A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

Q: 1-find both first partial derivatives  f(x,y)=x^2 e^xy

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

Q: 3. Determine the standard matrix of a linear transformation in 3D that rotates a vector…

A: Given: Let us consider, Axis =300,Projects on plane x=2y

Q: Solve the boundary-value problem y" – 8y' + 16y = 0 y(0) = 2 y(1) = 0 %3D - Use a as your…

A: We First find the auxiliary equation then its roots  at then provide the general solution of the…

Q: Q1 (C) Let a and k be constants. By implementing partial derivatives, prove that the function u…

A:

Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the  question does not make an…

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: If L(x, y, y/) = y² (1+ (y/)²)³ what are Ly and Ly? O Ly = 2y(1+ (y)²)³ and Ly = 6y"y² (1+ (y')²)² O…

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Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

Q: f(1) = 4 s' (1) = -2 g (3) = 7 gʻ (3) = 1 The point (1, 3) lies on the curve in the xy-plane given…

A: f(1) = 4 f'(1) = -2 g(3) = 7 g'(3) = 1 f(x)g(y) = 24 + x + y

Q: Find the solution to the initial-boundary value problem: 20u u(0, t) = u(1, t) = 0, u(x, 0) = 2x, du…

A: Given                      ∂u∂t=2∂2u∂x2,     0&lt;x&lt;1, t&gt;0,                  (1)…

Q: ",=a'u, O0 (19) (0.1) = 0, (L)= u(z,0) = S()

A: Note: According to our guideline policies we can answer only first question. (19) This question is…

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

A:

Q: Solve PDE 1 = e=*t u. u̟ =e¯*t Xx k (o0) u(0,t) =0 u(L,t) = 0 u(x,0) = L -x?

A: The given PDE is,uxx-1kut=e-xt

Q: I' = - R – I +2 (1) (2) R' = I (d) Which term in equations (1) and (2) do you think in an indirect…

A:

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Əz x²y + 7y²z + xz² = 9 ax'

A:

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

A:

Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

A:

Q: Use the separation of variables to find the general solution to dy/dt = (3t + 2)*y^(4) Be sure to…

A: We have to find the general solution to the differential equationdydt=(3t+2).y4

Q: Solve the non-homogenous system Sa' = -x – y+ 3/2 ly = 2x – 4y Find lim-00 r(t)

A:

Q: Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) +…

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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.