v tan x y(0)=1? 1+y Which of the following is the solution of the initial value problem y' A-) In/cot x|- In|y|- y =1 In cos 저+ Inl+y=1 В-) In sin x|+ In|y+y =1 C-) In tan x| + In|y| = 1 D-) In/cos x+ y =1 E-)

Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

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Q: The general solution of the differential equation // Die algemene oplossing van die…

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Q: 6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/s…

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Q: 2. Solve the Initial - Boundary Value Problem, Ии — а?ии — 0, for 0<x< 1, 0 <t <o∞ u(0, t) и(1,t) %—…

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Q: Express the ODE æ''+x = tan(t) as a system of first order differential equations: r' = y y' = Now…

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Q: The indicated functions are known linearly independent solutions of the associated homogeneous…

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Q: the DE X^4Y''+LAMBDA(Y)=0

A: We have given the Differential equation , x4y"+λy=0 has an irregular singular point at x=0

Q: Example: ux-Uy=u passes through (s,s,sin s) then number of solution of this partial differential…

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Q: Find the largest interval centered about x = 0 for which the given initial-value problem has a…

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Q: - (Ax + B) - Ar + B where A = acz and B = bez. When i--a 0, the differential equation becomes X* +…

A: By using relationship between trigonometric, hyperbolic and exponential functions you can solve the…

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A: To solve the problem we use the method of Laplace transformation also Laplace inverse transformation…

Q: 6. Let u (x, t) be the solution of the initial-boundary value problem U = 0 0, Uz (0, t) = ux (4,…

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Q: Determine a region of the xy-plane for which the given differential equation would have a point (x,,…

A: Existence and Uniqueness theorem: The initial value problem y'=f(x,y) has at least one solution on…

Q: A circuit consists of a resistor of resistance R and a capacitor of capacitance C, connected in…

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Q: A rectangular steel sheet is bounded by the axis -0y-0,x-a and y b. The temperature along the edge…

A: Steady state heat equation.

Q: The indicated functions are known linearly independent solutions of the associated homogeneous…

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Q: In the Laplace (or potential) equation: ux + Uyy = 0, the solutior u(x, y), which represerts…

A: Given, uxx+uyy=0, 0≤x≤1, 0≤y≤2....1 With boundary conditions, ux,0=0, ux,2=x1-x, 0&lt;x&lt;100,y=0,…

Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: Assume that the function f : R → R is differentiable. 1. Show that the function u(x, y) = f(x+y)e¬¤…

A: (1) To show:  u(x,y)=f(x+y)e-x is a solution of ∂u∂x-∂u∂y=-u. (2) To find: A function f such that…

Q: Determine the longest interval in which the initial value problem is certain to have a unique twice…

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Q: a) A flexible string of length is tightly stretched between x = 0, x = π, on x-axis, its ends being…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature…

A: Answer is given below

Q: 2. (a) Find particular integral of the partial differential equation ysin(x). (b) Find general…

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Q: The solution of variable separable differential equation -1+y* is %3D dx 1+x² a) tan y =tan x+c b)…

A: As per our guidelines I am solving one question. Please resubmit other question.  I am solving…

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

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Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: 9. A thin homogeneous bar of length L has initial tem- perature f(x) = Bx/L, with B a positive…

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Q: Consider the partial differential equation u at' vith boundary conditions u(0, t) = 0 and u(7, t) =…

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Q: 3. A thermally conducting solid bounded by two concentric spheres of radii a and b, a<b, is such…

A: Given that the temperature of the inner surface is T1 The temperature of the outer surface is…

Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: The linear and homogeneous differential equation of order 2 with coefficients in the range (a, b) is…

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Q: Determine the longest interval in which the initial value problem is certain to have a unique twice…

A: By the Existence and Uniqueness theorem we know that

Q: It can be shown that y, = 2 and y, = cos²(9x) + sin²(9x) are solutions to the differential equation…

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Q: ди 10²u = It 40x²¹ together with the boundary conditions u(0, t) = 0 and u(, t) = 0 for t≥0 and the…

A: Given eq. is ∂u∂t=14∂2u∂x2      (1)  u0,t=0, uπ2,t=0  for t≥0 ux,0=xπ2-x  for 0&lt;x&lt;π2

Q: 5. A handheld calculator will suffice for this problem, an initial value problem and its exace…

A: The fourth order Runge-kutta method uses the formulas below to perform the iterations and to…

Q: 2. Consider a homogeneous differential equation, p(т, у) dx + q(z, у) dy %3D 0, where the…

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Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

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Q: Example 10: Form the partial differential equation by eliminating the arbitrary constan a and b…

A: We can find the answer as below

Q: determine the longest interval in which the given initial value problem is certain to have a unique…

A: Given :   Differential eqution  is = y''+(cost)y'+3(ln|t|)y = 0…

Q: 4 y1 -x-12 cos x, y2-x-1/2 sin x y + xy +(-)y- are 2 homogenuous solutions of the DE and the…

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

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Q: how that an implicit solution of 2x sin2(y) dx – (x² + 11) cos(y) dy = 0 X - given by In(x + 11) +…

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Q: A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x'…

A: We are given the following PDE:                   ut(x, t)=5uxx(x, t), 0&lt;x&lt;1, t&gt;0Initial…

Q: Let u (x, t) be the solution of the initial-boundary value problem Ut 0 0, Uz (0, t) = uz (4, t) =…

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Q: 2. Solve Un Uxx X> 0,t> 0 with initial and boundary conditions given as u(x,0) = 1- exp(-x), u(x,0)…

A: The D'Alembert's solution of one dimensional wave equation whose charactertics lines are ξ0=x-ct and…

Q: The temperature u(x, t) of a metal bar of length (= 2 at a distance r from one end and at time t is…

A: Image is attached with detailed solution.

Q: Consider the initial value problem y' = -ty +0.1y°, y(0) = a, where %3D a is a given number. a) Use…

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Q: On what region of the xy-plane does the differential equation would have a unique solution wi…

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Q: The indicated functions are known linearly independent solutions of the associated homogeneous…

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Q: A direction field for the differential equation y' = cos(y) – sin(x) is given %3D below. a) Sketch…

A: Introduction: Every first-order ordinary differential equation has a slope field. The slope field is…

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.