Q4. Solve the heat equation subject to the given conditions: du 00 ax? at' du (0,t)=D0, Jx du (T,t)3D0, t>0 u(x,0)%3D-5x

Q: 1. Complete the table below. Ordinary or Partial Independent Variable Dependent Variable Linear or…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. A) y(t) = sin…

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Q: 21. Determine the largest interval on which a unique solution of the following initial value problem…

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Q: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

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Q: (B): Find the general solution of O.D.E y" – y = sinh(x) + cosh(x)

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Q: 24) Using Taylor method of order 2 to estimate the solution of the ODE y' = cos (xy?) ,y(1) = 2, h =…

A: To estimate the solution of ODE we will use the following Taylor's series formula for second order:…

Q: 1. y(y+k)² In sin(x) = y' tan x 2. y (x-7)y' = xy+3y %3D

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Q: 36. Y(t)-Y(t) = et, Y(0) = 0, Y'(0) = 0, √ "(0) = 0. 51/3 √3)

A: As per the guidelines I am answering only one question at a time. #36] y'''-y=et,…

Q: The following are three different methods for solving y (t) = f(t, y(t)): (A) Yn+1 = Yn + ¥ [S(tn,…

A: Given : three different methods for solving y't=ft,yt : A yn+1=yn+∆t2ftn,yn+ftn+∆t, yn+∆t ftn,ynB…

Q: dy = f'(x)dx: 1. y = In (1+x²) %3D

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

Q: ssint, 0<t < TI 0, t2 Tt , y(0) = 0 y'(0) = 0 5. Find the solution of the IVP y"+ y' +y : %3D

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Q: (35 points) 3. Solve the following 2nd order ODE's. a) 2y" =y'+6y, with y(0) =1 and y'(0) = 0. b)…

A: Given

Q: 1. A particle travels with acceleration ā = 2e-t i+5 cos t j – 3 sin t k. If the initial (i.e. at…

A: given  acceleration a→=2e-ti^+5costj^-3sintk^ at t=0 , initial position of the particle is 1,-3,2…

Q: Find the particular solution of the nonhomogeneous ODE. y"-4y' + 3y = x² + e* + sin2x

A: We will find out the required particular solution.

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

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Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: 2y + y = 0 subject to y(0) = 3, y' (0) = 2 y" - 4y +13y = 0 subject to y(0) = −1 y' (0) = 2 y' -9y=0…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: b) Find the potential P(x,y) attached to the exact ODE 2x sin(y) + x² cos(y) y' = 0 %3D

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Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: If Z= x Ln (xy) +y³ and y = cos(x²+1) find dZ ? dz dx

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Q: 2. Solve the following initial Condition Problems: dy а. dx Vry, y(1) = 2. || b. y' = x + y, y(0) =…

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Q: (e). Solve the following initial value problem (1) 6y" – y' – y = 0, y(0) = 10, y' (0) = 0 (ii). dy…

A: Using linear differential equation for ex I) And variable separable method for ex ii)

Q: 4. Find dw/dt. 3 (a) w = 5x²y*z4; x = P; y = t z = t5 1 (b) w = 5 cos.ry- sin rz; = X pi y = t := 1?…

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Q: 1. y"+y'-6y= -10-

A: As per our guideline we can solve only first question for you. Since all are separated questions.…

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: Given that y = cos(ln r), y2 = sin(ln r) are solutions of the homogeneous equation corresponding %3D…

A: Given: y1=cos(ln x) , y2=sin(ln x)  are solutions of…

Q: Calculate. for z = 4x² + 3y², x = sin(t), y = cos(t)

A: We will use chain rule for total derivative  If z is a function of x,y . Where as  x and y are…

Q: ercise: Solve the following differenti dy 1. dr dy 2. (x² – 1) + 2xy = 1 dx 3. e"secy dy = dx + xdy…

A: We have to find the solution of  linear differential equation

Q: a) dx² d²y + 9y = -2e3x „y(0) = 1 ,y' = 1 dx

A: From the given differential equation: d2ydx2-6dydx+9y=-2e3x So, we can also write as; D2-6D+9y=-2e3x…

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.