a2u a2u =4 at2 au(x,0) où 0 sxs2 with (0,t) = u(2,t) = 0, = 0, %3D %3D %3D at x if 0

Q: dy - te-, y(1) =0 dt Solve the Initial Value Problem:

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Q: 3. If only one person is on the swing in the image below, it is comparable to a point load of F =…

A: Given; F=500N x=0.5m length of the branch= 1.5m I=1* 10^-6 m^4 E=2*10^9 Nm^-2   the boundary…

Q: Consider the IVP dy/dt = (2-t)/(y+2) where y(0)=1.  Find a formula for the solution. State the…

A: In this question, we find a formula for the solution. i.e. y(t) State the domain of the definition…

Q: Solve the initial value problem dx 2x cos(4t) - dt with x(0) = 1. x(t) = = sqrt(-1/4sin(4t)+1) Hint:…

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Q: 2. Let y(x) = tan r. Show that y is the solution to the initial-value problem %3D dy =1+ y, y(0) =…

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Q: dx 5x cos(3t) dt with x(0) = -4.

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Q: Solve the partial differential equation: a²u =²; by the method of separation of variables for a…

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Q: Example:- Find the general solution of 1) xdy – ydx = 0 2) xcosh(y)dy – sinh (y) dx = 0 3)2dx –…

A: We need to find general solutions.

Q: dy (2y-2) %3D dx

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Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

A: Solution

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

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Q: 3. Sketch solution curves for a variety of initial conditions for dw = (w - 3)(w – 7). dt

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Q: Solve the initial-value problem with the initial condition Yo = 0. dy y + 3 dt %3D y =

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Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: 3. Prove that the IVP dy x- = cos(xy), y(1) = 2, dx has a unique solution curve locally near the…

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Q: I Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy. 2xy + e*…

A: Given y' =(2xy + e^x)/(x² + x e^x), initial point y(1)=0 To find y(1.2) and y(1.4)  Let step size h…

Q: A cylindrical homogenous, isotropic rod with insulated sides has the temperature f(x) L/2 ={L-X…

A: Given that, A cylindrical homogenous, isotropic rod with the insulated sides has the temperature,…

Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: The indicated function y. (x) is a solution of the given differential eguation. Use reduction of…

A: Second order Homogeneous differential equation

Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: The approximate value of y(3) for the initial value problem for dy/dx = cos(t) +sin(t), y(0)=0.5…

A: 4th order Range-Kutta method: The solution of y'=f(t, y), y(t0)=y0 is given by,…

Q: 2.Find the solution to dx using h=0.1 and h=0.05 Estimate the accuracy of second computation ²-y²,…

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Q: (a) Find the general solution of the equation (x – 2) + dy 3(x – 1) -y = 1 dx (x + 1) (b) Given the…

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Q: 1.) Determine the Region in the xy plane for the differential equation dy/dx = cuberoot(xy) would…

A: Part (a) From the given information. The differential equation is as follows. dydx=xy3

Q: Solve the initial value problem: cos z – 3x?y – 2æ) dx + (2y sin x – x° + In y) dy = 0; y (0) - -- -…

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Q: The formation of the partial differential equation by eliminating arbitrary function of z= 3f(x³ –…

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Q: Consider the initial value problem dt = 5 – y, y(0) = 2. Use Euler's method and take three steps to…

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Q: 3. Approximate the solution to the partial differential equation a²u ²u 5л 0x2 (x, y) + dyz (x, y) —…

A: Given: ∂2u∂x2x,y+∂2u∂y2x,y-12.5π2ux,y=-25π2sin5π2xsin5π2y To find: Dirichlet boundary condition

Q: 5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium…

A: Given the heat equation is k∂2u∂x2-hu=∂u∂t, 0<x<L, t>0 The initial temperature is f(x)…

Q: ) Solve the partial differential equation problem U = 16uxx, 0 0 Boundary conditions: u(0, t) =…

A: Given PDE is utt=16uxx,   0<x<1,   t>0 Boundary conditions: u(0,t)=u(1,t)=0 Initial…

Q: What is the solution of given initial value problem? =y + sin t dt2 da + cost dt - dt2 * (0) = 1, a…

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Q: 10 % Find the absolute minimum and ab- solute maximum of y = cos²t-cost on the Cos? 2T interval [0,…

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Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . y"…

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Q: dy Q2/ Use Euler's method to solve + 1.2y = 7e-0.3x from x = 0 to x = 2 with the initial dx…

A: Given dydx+1.2y=7e-0.3x

Q: 3- Find the solution of given initial value problem: y" +y= u3(t), y(0) = 1, y'(0) = 0 y(t) = sint +…

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Q: Find the particular solution of the equation 2(x +3) dy – xy dx = 0 %3D - tisfying the initial…

A: Given: 2(x+3)dy-xydx=0     satisfying the intial condition x=-2 and y=1

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: Two particles A and B, of masses 0-3 kg and 0-7 kg, are moving towards each other on a smooth…

A: Given that masses of particles are                                                      mA=0.3…

Q: 2. Given y' = x² + y . With y=-1 when x=0. b. Calculate y(0.4) and y(0.6) using modified Euler…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: Solve the partial differential equation: a²u azu by the method of separation of variables for a…

A: Given: ∂2u∂t2=c2∂2u∂x2 To find: ux,t=0

Q: Q-1-) Eind the general solution of the given Ordinary Differential Egauations system: X'(t) = *(1)…

A: Given: X¯'(t) =3-94-3X(t) where X¯(t) =x1(t)x2(t) To find: General solution of given system of…

Q: Rewrite y" - 2y + y² = cos x as two first-order equations and then use Euler's method to integrate…

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Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

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: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

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Q: dy + [2 In(t – 1)] y = ed-3 – 1' 3 V16 – t2 y(2) = 1. dt Determine the largest interval of t in…

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Q: Consider the initial value problem * = (tan (z + y))² y (0) = 0 %3D What is limg-1 y (x)?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.