1. The coordinate of a point undergoing rectilinear motion is given by x(t) = t³ – 4t, -2

Q: Let y (t) be the solution of the initial value problem y"-4y +5y =e-2t 1 y (0) and y(0) = 17 %3D 17…

A: To find  The asymptotic behaviours as t tends to infinity.

Q: 2.22. Plot the curve Yk+1 = y% – 2yk + 2 and analyze the stability of any fixed points. Show that…

A: Given, yk+1=yk2-2yk+2...1 We can write the given equation as, fx=x2-2x+2...2 Now, finding the fixed…

Q: 3.) Use the Maximum/Minimum Principles to deduce that the solution u of the problem D.E. ut = kuzr…

A: given differential equation ut=kuxx    ...i where 0≤x≤π, t≥0 boundary condition u0,t=0       uπ,t=0…

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: Solve the initial value problem for an arbitrary f(t) function. y"+4y'+4y=f(t),  y(0)=2 ,  y'(0) =…

A:

Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

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

A: The heat equation given is as follows: k∂2u∂x2-hu=∂u∂t, 0<x<L,…

Q: Let y be the solution of the initial value problem y′′+y=−sin(2x), y(0)=0, y′(0)=0. Find the maximum…

A: Here, differential equation is y’’+y=-sin2x

Q: 4. Find the points on x² + y² + z² = 25, %3D where the temperature T(x, y, z) = x² + 4y² + 9z², is…

A:

Q: Solve the following initial value problem (t2-22t+105)(dy/dt)=y with y(11)=1 Find y as a function of…

A: According to the given information it is required to solve the given initial value problem:

Q: 4) The position function of a particle is given by F(t) = (t², 5t, tť² – 2t). When is the speed a…

A:

Q: At what time t does the speed of a particle moving in 3-space with position function r(t) = ti+tj+…

A: To find the time at which the speed of the partial is minimum. Note that, the velocity is the time…

Q: This is a differential equations problem.

A:

Q: 2.- The determines the undamped forced oscillations of a mass on a spring. The values of mass m,…

A: Answer

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

A:

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

A:

Q: 1. Find the orthogonal trajectories of the family of curve a2+3y2 = cy ,where c is an arbitrary…

A:

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

A:

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: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

A:

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: What are the equilibrium solutions of the DE dy /dt=−3(2−y)?

A: given DE  is dydt=-3(2-y)

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: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: We have to find the equation of motion for given condition.

Q: Given the one-parameter family of curves y² = Cx³ + 5. Find the family of orthogonal trajectories.…

A:

Q: 6. Consider the problem u; + u²ux = 0, |x| 0 satisfying the initial condition u(x,0) = %3D 1+x2 a.…

A: The complete solutions are given below

Q: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: 4. An imaginary ant is walking on an imaginary cartesian plane so that at any point (x, y) it moves…

A:

Q: Verify that u(r, t) = f(e-"x) solves the initial value problem (au + z8,u = 0, u(x,0) = f(z).

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then…

A: NOTE: Refresh your page if you can't see any equations. . mass is m=1 kg the spring constant is k=24…

Q: Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u,…

A: In this question, we solve the heat equation by using the separation of varibale. U(x,t)=X(x)T(t).

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 15 The curve y=x'+ px² +qx+r passes through the point (0, 5) and has stationary points at x= 4 and…

A: The given curve is f(x) =x3 +px2 +qx + r This curve passes through (0,5) hence it will satisfy And…

Q: Assume that 0 < Po < M in equation dP 3D КP(М - Р), Р(0) — Ро. dt (a) Find the equilibrium points…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: 15 The curve y=xr'+px² +qx+r passes through the point (0, 5) and has stationary points at x= 4 and…

A: The given curve is  f(x) = x3 + px2 +qx + r The stationary points are that points where the curve…

Q: Sketch, by hand (without using any graphing device), several trajectories in the phase…

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Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

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

A:

Q: solve the Cauchy problem on the real line for the given initial position and velocity functions and…

A: Given that, and ,  By the Cauchy problem ,

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

A: Given suppose heat is lost from the lateral surface of a thin rod of length L in to a surrounding…

Q: By solving Laplace equation in 2D, determine the steady state temperature of a thin rectangular…

A: Let, at any point (x,y) the temperature of the plate be u(x,y). It is given that u(x,y) satisfies…

Q: (j) Suppose that the solution of the initial value problem u" + u = 0.5 cost, u(0) = 0, u'(0) = 0 is…

A:

Q: Solve equation (4) in Section 5.2 EI dY = w(x) dx4 (4) subject to the appropriate boundary…

A: To solve the below differential equation. EId4ydx4=wx Here wx=w0x, 0&lt;x&lt;l, and the beam is…

Q: Determine the constants c and d in the equation of the curve y = ax + b³ + cx+d having a critical…

A:

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.