5. Solve the initial-boundary value problem u(x, t) = c²u(x, t) for 0 0; u(x, 0) = sin 2x; u₁(x,0) = re-²; u(0, t) = 0 for all t > 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.

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A: Introduction: A linear approximation is a mathematical term that refers to the use of a linear…

Q: 6. For what values of y(0) will the solution of y' = y(y – 2),x > 0 a) be a constant function b) be…

A: First of all we draw the direction field of the differential equation y' = y(y-2)

Q: 2. Find the general solution of x*v + 1) dx + y'(x - 1) dy = 0 x2 - y? + 2x - 2y + А. 2ln[(y + 1)/(x…

A: No option is matching the final answer. All the given four options are incorrect. The correct answer…

Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

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: Let y' = y(y-3) Use Euler's method to approximate y(1) for the function y satisfying y'=y(y-3) and…

A:

Q: 14. If f(z) = 2 + ² -r', then the equation S(z) = 0has a solution on the interval A [1,2] B (0,1] c…

A: Given equation, fx=2+x2-x3, To find the interval on which the equation fx=0 has a solution.

Q: The slope field for y' = x - xy is given below. Sketch the solution that satisfies the condition…

A:

Q: 4. If we use the center difference formula for y" Yi+1 y" (x₂) and the midpoint difference formula…

A:

Q: Let u = (x,t) represent the temperature of a hose with length L. The temperature with t= 0 is u(x,0)…

A: To solve following PDE using method of separation of variables :      ut=α2uxx ,  0&lt;x&lt;L,…

Q: y''+2y'+2y=r(t), where: r(t)={10sin2t if 0π ; y(0)=1 ; y'(0)=-5

A:

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

A:

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: Let x, y be the unique solution of x' = y y' = 0, y(0) = 1. = -x x (0) Show that x, y verify x2 + y?…

A: Given x' = y                   (1)y' = -x                (2)x(0) = 0                    (3)y(0) = 1…

Q: x'= -2y, y'= -4x, where primes indicate derivatives with respect to t, that satisfies the initial…

A:

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

A:

Q: Solve y"+10y+26y= y(0) = y'(0) = 0 <t<3 t3 or t<1 Give the solution for 1 ≤ t< 3 y(t) =

A:

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: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

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

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3  (a) Use Euler's Method with time step…

A: Euler's method is a technique for numerical differentiation in which we compute the approximation of…

Q: Find all functions that form a fundamental set of solutions for t2y" – 2ty' + 2y = 0. O y(t) = et O…

A: We have to solve given problem:

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

A:

Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

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

A:

Q: dt, then F'(x) = 0 a) If F(x) = √5 / / di 20 3 b) If F(x) = ² = dt, then F'(x) = c) If F(x) = √²/1/1…

A: Given:   a) Fx=∫20x1tdt      we use common integral ∫1tdt=lnt          =lnt20x          Fx=lnx-ln20…

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

A:

Q: The interval in wh (4-t2)y' +2ty 3 Select one: O a. (-2,2) b. (0,1) C. (0,2) d. NOTA

A: Given        4-t2y'+2ty=3t2;     y(1)=5

Q: Calculate the linear approximation for f(x): f(x) × f(a) + f'(a)(x - a). 3 at a = 1 f(x) = 2+x L(x)…

A: