ди a2u Solve the heat-conduction equation at c2 in a bar subject to the boundary conditions: (a) u(0, t) = 0 (t 2 0) (the end x = 0 is held at zero temperature); (b) u(1, t) = 1 (t > 0) (the end x = 1 is at temperature 1) c) u(x, 0) = x(2 – x) (0

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

A: This is a problem of Differential Geometry.

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: Solve X [1]-[-4⁰ Ly'. x(t) = y(t) = 3 2 3] [] x(0) = −4, y(0) = 32 -40 -13

A: From the given homogeneous equation:

Q: Use the method of reduction of order to find a second solution to ty''−(6t+4)y'+(9t+12)y=0,  t>0…

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Q: (b) y'+y=f(t), y(0) = 0, where f(t) = 0 for 0 ≤ t < 1 and f(t) = 5 for t ≥1.

A: The given differential equation is , .Where .We know that a differentiable function is continuous as…

Q: g- y" + 2y' + 5y= 2u(t) where: y(0)= y'(0)= 0, u(t) = a*e-bt {a and b are constants} %3D

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Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Solve the IVP 2y"+5y'-3y=0 y(0)=-5 y'(0)=29 y(x)=?

A: The given differential equation is                                                   2y''+5y'-3y=0…

Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: Solve y"-2y+ly = 0, y(0) = −1, y'(0) = 1 y(t) =

A: Solution of the differential equations using Lapalce transfermation

Q: Solve (1 07 y'' – 4y' + 3y y(0) = y'(0) = 0 y(t) = f(t)uo(t) - g(t)u7(t), where f(t) = g(t) =

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Q: Solve y''+ 4y = 8(t – 3), y(0) = y'(0) = 0

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Q: So I am given the problem: y'= (t+y)^2(y^2)+ sin(y^3) +ye^(ty), y(0) = 0   This initial value…

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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 the particular solution using separation of variables that satisfies the initial condition

A: Step 1:Step 2: Step 3: Step 4:

Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

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Q: Suppose that y' = f(y) has no constant solutions, where f : R -> R is infinitely many times…

A: Consider the provided question,

Q: Consider the following initial value problem: Edit y" + 4y' + 20y = d(t – 1); y(0) = 1, y'(0) = 0 a)…

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Q: wo functions: y_1 = x^2 , y_2 = 1/x^2 are complementary solutions to the equation: x^2 y" + xy' - 4y…

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Q: If y1 and y2 two solutions of (1 – a²)y" – 2xy' + n(n+1)y = 0; -1<x < 1 Show that W (y1, Y2) : 1-…

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Q: Solve Ut=a²uxx, 0<x<L, ur(0, t) = 0, ux (L, t) = 0, u(x,0) = f(x).

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Q: Find the solution of: y" +y=2e' ,y(0) = 0, y'(0) = 0 Select one: O a. y = sint – 2cost + e' O b. y =…

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

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Q: 3. y"+2y' +y = 2 sin t H(t – x1), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost + (t+1-1)e"-']H(t-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: y" – y' = sin(t) y(0) = 1 y' (0) = -1

A: We have to solve the IVP           y''-y'=sinty0=1y'0=-1